FAQ Coverage Gaps

Generated: 2025-11-14

Concepts from the learning graph (200 total concepts) not adequately covered in the current FAQ.

Summary Statistics

Total Concepts in Learning Graph: 200
Concepts Covered in FAQ: 130 (65%)
Concepts with Gaps: 70 (35%)
Critical Gaps (High Priority): 24 concepts
Medium Priority Gaps: 28 concepts
Low Priority Gaps: 18 concepts

Critical Gaps (High Priority)

These are fundamental concepts that many students need help with and should be added to the FAQ immediately.

Triangle Congruence and Properties (12 concepts)

1. SSS Congruence

Centrality: High (prerequisite for many triangle proofs)
Current Coverage: Mentioned in passing, no dedicated FAQ question
Suggested Question: "What is SSS congruence and when do I use it?"
Suggested Answer Focus: Definition (three pairs of corresponding sides congruent → triangles congruent), visual example, when to apply, how to prove with SSS

2. SAS Congruence

Centrality: High (commonly used congruence theorem)
Current Coverage: Mentioned but no details
Suggested Question: "What is SAS congruence and how is it different from SSS?"
Suggested Answer Focus: Definition (two sides and included angle), why included angle matters, examples, common mistakes

3. ASA Congruence

Centrality: High (key theorem for many proofs)
Current Coverage: Mentioned but no explanation
Suggested Question: "What is ASA congruence?"
Suggested Answer Focus: Definition (two angles and included side), relationship to AAS, when to use

4. AAS Congruence

Centrality: Medium-High (useful alternative to ASA)
Current Coverage: Mentioned in list
Suggested Question: "What is AAS congruence and how does it differ from ASA?"
Suggested Answer Focus: Definition, why non-included side works, Triangle Sum Theorem connection

5. HL Congruence

Centrality: Medium-High (specific to right triangles)
Current Coverage: Mentioned in list
Suggested Question: "What is HL congruence for right triangles?"
Suggested Answer Focus: Hypotenuse-Leg theorem, why it only works for right triangles, applications

6. CPCTC

Centrality: High (essential for using congruence in proofs)
Current Coverage: None
Suggested Question: "What does CPCTC mean and when do I use it?"
Suggested Answer Focus: Corresponding Parts of Congruent Triangles are Congruent, how to use after proving congruence, examples in proofs

7. Triangle Sum Theorem

Centrality: Very High (fundamental property)
Current Coverage: Mentioned but no dedicated question
Suggested Question: "Why do the angles in a triangle always add up to 180°?"
Suggested Answer Focus: Theorem statement, proof idea using parallel lines, applications, examples

8. Exterior Angle Theorem

Centrality: High (commonly used in proofs)
Current Coverage: None
Suggested Question: "What is the Exterior Angle Theorem?"
Suggested Answer Focus: Exterior angle equals sum of remote interior angles, proof, applications

9. Triangle Inequality Theorem

Centrality: High (determines if triangle can exist)
Current Coverage: Mentioned in theorem list
Suggested Question: "What is the Triangle Inequality Theorem and why is it important?"
Suggested Answer Focus: Sum of two sides must be greater than third side, why this matters, examples of impossible triangles

10. Isosceles Triangle Theorem

Centrality: High (fundamental property)
Current Coverage: None
Suggested Question: "What is special about isosceles triangles?"
Suggested Answer Focus: Base angles are congruent, converse (if base angles congruent → isosceles), applications

11. Base Angles Theorem

Centrality: Medium-High (specific to isosceles triangles)
Current Coverage: Mentioned but no details
Suggested Question: "What are base angles in an isosceles triangle?"
Suggested Answer Focus: Definition, theorem (base angles congruent), how to identify base vs vertex angle

12. Equilateral Triangle Properties

Centrality: Medium (special case of isosceles)
Current Coverage: Used in examples but no dedicated question
Suggested Question: "What are the properties of equilateral triangles?"
Suggested Answer Focus: All sides equal, all angles 60°, relationship to isosceles, applications

Area and Volume Formulas (6 concepts)

13. Area of Rectangle

Centrality: High (basic formula)
Current Coverage: None
Suggested Question: "How do I find the area of a rectangle?"
Suggested Answer Focus: Formula A = lw, why it works, relationship to square area

14. Area of Triangle

Centrality: High (fundamental formula)
Current Coverage: None
Suggested Question: "How do I calculate the area of a triangle?"
Suggested Answer Focus: Formula A = ½bh, why ½ (half of rectangle), different ways to choose base and height

15. Area of Circle

Centrality: High (important formula)
Current Coverage: None
Suggested Question: "What is the formula for the area of a circle?"
Suggested Answer Focus: Formula A = πr², relationship to circumference, why π appears

16. Volume of Prism

Centrality: High (basic 3D formula)
Current Coverage: Mentioned but no details
Suggested Question: "How do I find the volume of a prism?"
Suggested Answer Focus: Formula V = Bh (base area × height), works for all prisms, examples

17. Volume of Cylinder

Centrality: High (common 3D shape)
Current Coverage: Mentioned but no details
Suggested Question: "What is the formula for the volume of a cylinder?"
Suggested Answer Focus: Formula V = πr²h, relationship to prism formula, applications

18. Volume of Sphere

Centrality: Medium-High (important 3D formula)
Current Coverage: Mentioned in lists
Suggested Question: "How do I calculate the volume of a sphere?"
Suggested Answer Focus: Formula V = (4/3)πr³, why (4/3) coefficient, real-world applications

Triangle Centers (4 concepts)

19. Centroid

Centrality: Medium-High (important triangle center)
Current Coverage: Mentioned in course overview
Suggested Question: "What is the centroid of a triangle?"
Suggested Answer Focus: Intersection of medians, center of mass, divides medians 2:1, how to find

20. Incenter

Centrality: Medium-High (center of inscribed circle)
Current Coverage: Mentioned in passing
Suggested Question: "What is the incenter and how is it used?"
Suggested Answer Focus: Intersection of angle bisectors, center of inscribed circle, equidistant from sides

21. Circumcenter

Centrality: Medium-High (center of circumscribed circle)
Current Coverage: Mentioned in passing
Suggested Question: "What is the circumcenter of a triangle?"
Suggested Answer Focus: Intersection of perpendicular bisectors, center of circumscribed circle, equidistant from vertices

22. Orthocenter

Centrality: Medium (intersection of altitudes)
Current Coverage: Mentioned in passing
Suggested Question: "What is the orthocenter and where is it located?"
Suggested Answer Focus: Intersection of altitudes, location varies by triangle type (acute/obtuse/right), relationship to other centers

Basic Terminology (2 concepts)

23. Ray (detailed)

Centrality: High (fundamental concept)
Current Coverage: Brief mention in line vs segment question
Suggested Question: "What is a ray in geometry?"
Suggested Answer Focus: Definition (endpoint, extends infinitely one direction), notation, examples, difference from line and segment

24. Vertex (detailed)

Centrality: High (appears throughout geometry)
Current Coverage: Mentioned in angle discussion but no dedicated question
Suggested Question: "What is a vertex?"
Suggested Answer Focus: Definition (corner point), use in angles, polygons, polyhedra, plural is vertices

Medium Priority Gaps (28 concepts)

These concepts would enhance the FAQ but are less urgent than critical gaps.

Quadrilateral Properties (9 concepts)

25. Parallelogram

Centrality: High (fundamental quadrilateral)
Current Coverage: None
Suggested Question: "What are the properties of a parallelogram?"
Suggested Answer Focus: Opposite sides parallel and congruent, opposite angles congruent, diagonals bisect each other, sufficient conditions

26. Rectangle

Centrality: High (common quadrilateral)
Current Coverage: Used in examples but no dedicated question
Suggested Question: "What makes a rectangle different from other parallelograms?"
Suggested Answer Focus: All angles are right angles, diagonals are congruent, special case of parallelogram

27. Rhombus

Centrality: Medium-High
Current Coverage: None
Suggested Question: "What is a rhombus and what are its properties?"
Suggested Answer Focus: All sides congruent, diagonals perpendicular, diagonals bisect angles, relationship to square

28. Square

Centrality: High (special quadrilateral)
Current Coverage: Used in examples but no dedicated question
Suggested Question: "Why is a square special?"
Suggested Answer Focus: Both rectangle and rhombus, all sides and angles equal, most restrictive quadrilateral properties

29. Trapezoid

Centrality: Medium
Current Coverage: None
Suggested Question: "What is a trapezoid?"
Suggested Answer Focus: One pair of parallel sides (bases), legs, median formula, area formula

30. Isosceles Trapezoid

Centrality: Medium
Current Coverage: None
Suggested Question: "What are the properties of an isosceles trapezoid?"
Suggested Answer Focus: Legs congruent, base angles congruent, diagonals congruent

31. Kite

Centrality: Low-Medium
Current Coverage: Mentioned in glossary only
Suggested Question: "What is a kite in geometry?"
Suggested Answer Focus: Two pairs of adjacent sides congruent, one pair of opposite angles congruent, diagonals perpendicular

32. Polygon Interior Angles

Centrality: High (important formula)
Current Coverage: None
Suggested Question: "How do I find the sum of interior angles in a polygon?"
Suggested Answer Focus: Formula (n-2)×180°, why it works, examples for different polygons

33. Regular Polygon

Centrality: Medium
Current Coverage: Mentioned in course overview
Suggested Question: "What is a regular polygon?"
Suggested Answer Focus: All sides congruent, all angles congruent, examples, interior angle formula for regular n-gon

Circle-Specific Concepts (9 concepts)

34. Central Angle

Centrality: High (basic circle concept)
Current Coverage: None
Suggested Question: "What is a central angle in a circle?"
Suggested Answer Focus: Vertex at center, sides are radii, measures same as intercepted arc

35. Inscribed Angle

Centrality: High (important theorem)
Current Coverage: None
Suggested Question: "What is an inscribed angle and how does it relate to the central angle?"
Suggested Answer Focus: Vertex on circle, sides are chords, measures half the intercepted arc, Inscribed Angle Theorem

36. Chord

Centrality: Medium-High
Current Coverage: Mentioned in glossary
Suggested Question: "What is a chord of a circle?"
Suggested Answer Focus: Segment with endpoints on circle, diameter is longest chord, perpendicular from center bisects chord

37. Tangent to Circle

Centrality: High (key circle concept)
Current Coverage: None
Suggested Question: "What is a tangent line to a circle?"
Suggested Answer Focus: Touches circle at exactly one point (point of tangency), perpendicular to radius at that point, applications

38. Secant

Centrality: Medium
Current Coverage: Mentioned in glossary
Suggested Question: "What is a secant line?"
Suggested Answer Focus: Line intersecting circle at two points, relationship to chords and tangents

39. Arc Length

Centrality: Medium-High (important measurement)
Current Coverage: Mentioned but no formula
Suggested Question: "How do I calculate arc length?"
Suggested Answer Focus: Formula (θ/360°)×2πr or θr (radians), relationship to circumference, examples

40. Sector

Centrality: Medium
Current Coverage: Mentioned but no details
Suggested Question: "What is a sector of a circle and how do I find its area?"
Suggested Answer Focus: Pie slice shape, area formula (θ/360°)×πr², relationship to circle area

41. Major Arc

Centrality: Low-Medium
Current Coverage: Mentioned in glossary
Suggested Question: "What is the difference between a major arc and a minor arc?"
Suggested Answer Focus: Major arc > 180°, minor arc < 180°, semicircle = 180°, naming conventions

42. Semicircle

Centrality: Medium
Current Coverage: None
Suggested Question: "What is a semicircle?"
Suggested Answer Focus: Half of a circle (180° arc), inscribed angle in semicircle is right angle (Thales' Theorem)

Triangle Parts and Relationships (6 concepts)

43. Median of Triangle

Centrality: Medium-High
Current Coverage: None
Suggested Question: "What is a median of a triangle?"
Suggested Answer Focus: Segment from vertex to midpoint of opposite side, three medians meet at centroid, divides triangle into equal areas

44. Altitude of Triangle

Centrality: Medium-High
Current Coverage: None
Suggested Question: "What is an altitude of a triangle?"
Suggested Answer Focus: Perpendicular segment from vertex to opposite side (or extension), used in area formula, three altitudes meet at orthocenter

45. Perpendicular Bisector of Triangle

Centrality: Medium
Current Coverage: General perpendicular bisector mentioned
Suggested Question: "What is the perpendicular bisector of a triangle side?"
Suggested Answer Focus: Perpendicular line through midpoint of side, three meet at circumcenter, all points equidistant from endpoints

46. Angle Bisector of Triangle

Centrality: Medium
Current Coverage: General angle bisector covered
Suggested Question: "What is special about angle bisectors in triangles?"
Suggested Answer Focus: Three angle bisectors meet at incenter, Angle Bisector Theorem (divides opposite side proportionally)

47. Hinge Theorem

Centrality: Low-Medium
Current Coverage: None
Suggested Question: "What is the Hinge Theorem?"
Suggested Answer Focus: Two triangles with two congruent sides: larger included angle → longer third side, converse also true

48. Third Angle Theorem

Centrality: Medium
Current Coverage: None
Suggested Question: "What is the Third Angle Theorem?"
Suggested Answer Focus: If two angles of one triangle are congruent to two angles of another, the third angles are congruent (follows from Triangle Sum)

Transformation Details (4 concepts)

49. Translation (detailed)

Centrality: High
Current Coverage: Defined but could expand
Suggested Question: "How do I perform a translation in coordinate geometry?"
Suggested Answer Focus: Add same values to all coordinates: (x,y) → (x+a, y+b), preserves everything, notation

50. Rotation (detailed)

Centrality: High
Current Coverage: Defined but could expand
Suggested Question: "How do rotations work in geometry?"
Suggested Answer Focus: Fixed center point, angle and direction, 90°/180°/270° are common, formulas for rotation about origin

51. Reflection (detailed)

Centrality: High
Current Coverage: Defined but could expand
Suggested Question: "How do I reflect a figure over a line?"
Suggested Answer Focus: Mirror image, perpendicular distance preserved, common lines (x-axis, y-axis, y=x), formulas

52. Composition of Transformations

Centrality: Medium-High
Current Coverage: None
Suggested Question: "What is a composition of transformations?"
Suggested Answer Focus: Performing multiple transformations in sequence, order matters (not commutative), glide reflection

Low Priority Gaps (18 concepts)

These concepts are more specialized or advanced and could be added as the FAQ expands.

Similarity and Proportions (7 concepts)

53. Scale Factor

Centrality: Medium
Current Coverage: Mentioned in dilation but no details
Suggested Question: "What is a scale factor in similar figures?"
Suggested Answer Focus: Ratio of corresponding lengths, how to find it, effect on perimeter and area

54. Similarity Ratio

Centrality: Medium
Current Coverage: None
Suggested Question: "What is a similarity ratio?"
Suggested Answer Focus: Ratio of corresponding parts in similar figures, same as scale factor, notation

55. AA Similarity

Centrality: High
Current Coverage: Mentioned in glossary
Suggested Question: "What is AA similarity?"
Suggested Answer Focus: Two angles congruent → triangles similar, most common similarity theorem, examples

56. SAS Similarity

Centrality: Medium
Current Coverage: None
Suggested Question: "What is SAS similarity for triangles?"
Suggested Answer Focus: Two sides proportional and included angle congruent → triangles similar, when to use

57. SSS Similarity

Centrality: Medium
Current Coverage: Mentioned in glossary
Suggested Question: "What is SSS similarity?"
Suggested Answer Focus: Three sides proportional → triangles similar, checking ratios, applications

58. Proportional Segments

Centrality: Medium
Current Coverage: None
Suggested Question: "What are proportional segments?"
Suggested Answer Focus: Segments with lengths in the same ratio, used in similarity, proportions in parallel line divisions

59. Geometric Mean

Centrality: Low-Medium
Current Coverage: None
Suggested Question: "What is the geometric mean in right triangles?"
Suggested Answer Focus: Altitude to hypotenuse creates geometric mean relationships, formula, applications

Advanced Right Triangle Topics (4 concepts)

60. Altitude to Hypotenuse

Centrality: Low-Medium
Current Coverage: None
Suggested Question: "What is special about the altitude to the hypotenuse?"
Suggested Answer Focus: Creates similar triangles, geometric mean relationships, used in proofs

61. Pythagorean Triple

Centrality: Medium
Current Coverage: None
Suggested Question: "What is a Pythagorean triple?"
Suggested Answer Focus: Three whole numbers satisfying a²+b²=c², common triples (3-4-5, 5-12-13, 8-15-17), multiples

62. Converse Pythagorean Theorem

Centrality: Medium
Current Coverage: None
Suggested Question: "What is the Converse of the Pythagorean Theorem?"
Suggested Answer Focus: If a²+b²=c² then triangle is right, how to test if triangle is right, why converse is useful

63. Distance in Coordinate Plane

Centrality: High
Current Coverage: Distance formula covered
Suggested Question: "How does the Distance Formula relate to the Pythagorean Theorem?"
Suggested Answer Focus: Distance formula is Pythagorean Theorem in coordinates, visual derivation, connection

Trigonometry Applications (3 concepts)

64. Angle of Elevation

Centrality: Medium
Current Coverage: Mentioned in glossary
Suggested Question: "What is an angle of elevation?"
Suggested Answer Focus: Angle above horizontal, measured from eye level, used in height problems, tangent ratio application

65. Angle of Depression

Centrality: Medium
Current Coverage: Mentioned in glossary
Suggested Question: "What is an angle of depression and how is it used?"
Suggested Answer Focus: Angle below horizontal, equals angle of elevation (alternate interior angles), applications

66. Indirect Measurement

Centrality: Medium
Current Coverage: Mentioned in topics
Suggested Question: "What is indirect measurement in geometry?"
Suggested Answer Focus: Finding measurements without direct measurement, using similar triangles or trigonometry, real-world applications

3D Geometry Details (4 concepts)

67. Cross-Section (expanded)

Centrality: Medium
Current Coverage: Cavalieri's Principle question mentions cross-sections
Suggested Question: "How do I identify cross-sections of 3D shapes?"
Suggested Answer Focus: Slice cylinder → circle or rectangle, slice cone → circle or triangle, examples for each solid

68. Net of Solid

Centrality: Low-Medium
Current Coverage: None
Suggested Question: "What is a net of a 3D solid?"
Suggested Answer Focus: 2D pattern that folds into 3D shape, helps visualize surface area, examples for cube, cylinder, pyramid

69. Volume of Pyramid

Centrality: Medium
Current Coverage: Mentioned but no dedicated question
Suggested Question: "What is the formula for the volume of a pyramid?"
Suggested Answer Focus: V = (1/3)Bh, why 1/3 (Cavalieri's Principle), any base shape works

70. Volume of Cone

Centrality: Medium
Current Coverage: Mentioned but no dedicated question
Suggested Question: "How do I find the volume of a cone?"
Suggested Answer Focus: V = (1/3)πr²h, special case of pyramid, relationship to cylinder

Recommendations

Phase 1: Critical Gaps (Immediate - Next 2 weeks)

Add 24 questions covering critical gaps:

Triangle Congruence (6 questions)
SSS, SAS, ASA, AAS, HL, CPCTC
Priority: Highest (used throughout course)
Triangle Theorems (6 questions)
Triangle Sum, Exterior Angle, Triangle Inequality, Isosceles Triangle, Base Angles, Equilateral properties
Priority: Highest (fundamental properties)
Area and Volume Formulas (6 questions)
Rectangle area, triangle area, circle area, prism volume, cylinder volume, sphere volume
Priority: Very High (essential calculations)
Triangle Centers (4 questions)
Centroid, incenter, circumcenter, orthocenter
Priority: High (special points)
Basic Terminology (2 questions)
Ray (detailed), Vertex (detailed)
Priority: High (foundational concepts)

Expected Impact: - Coverage increases from 65% to 77% - Closes most critical knowledge gaps - Provides essential theorem explanations - Enables students to complete triangle proofs

Phase 2: Medium Priority Gaps (1-2 months)

Add 28 questions covering medium priority gaps:

Quadrilateral Properties (9 questions)
Parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, kite, interior angles, regular polygons
Priority: High (polygon unit)
Circle-Specific Concepts (9 questions)
Central angle, inscribed angle, chord, tangent, secant, arc length, sector, major/minor arc, semicircle
Priority: High (circle unit)
Triangle Parts (6 questions)
Median, altitude, perpendicular bisector, angle bisector, Hinge Theorem, Third Angle Theorem
Priority: Medium-High (deeper triangle understanding)
Transformation Details (4 questions)
Translation (detailed), rotation (detailed), reflection (detailed), composition
Priority: Medium (transformation unit)

Expected Impact: - Coverage increases from 77% to 91% - Comprehensive polygon and circle coverage - Complete transformation understanding - Enhanced triangle knowledge

Phase 3: Low Priority Gaps (Long-term - 3-6 months)

Add 18 questions covering low priority gaps:

Similarity and Proportions (7 questions)
Scale factor, similarity ratio, AA/SAS/SSS similarity, proportional segments, geometric mean
Priority: Medium (similarity unit)
Advanced Right Triangle Topics (4 questions)
Altitude to hypotenuse, Pythagorean triples, Converse Pythagorean, distance-Pythagorean connection
Priority: Low-Medium (enrichment)
Trigonometry Applications (3 questions)
Angle of elevation, angle of depression, indirect measurement
Priority: Medium (trig applications)
3D Geometry Details (4 questions)
Cross-sections (expanded), nets, pyramid volume, cone volume
Priority: Low-Medium (3D visualization)

Expected Impact: - Coverage increases from 91% to 100% - Completely comprehensive FAQ - All 200 concepts addressed - Advanced topics covered

Priority Matrix

Must-Have (Critical Gaps - 24 questions)

These are essential for a functional FAQ that serves most student needs:

Concept Area	Questions	Impact	Difficulty
Triangle Congruence	6	Very High	Medium
Triangle Theorems	6	Very High	Medium
Area/Volume Formulas	6	Very High	Easy
Triangle Centers	4	High	Medium-Hard
Basic Terminology	2	High	Easy

Total: 24 questions → Brings coverage to 77%

Should-Have (Medium Priority - 28 questions)

These significantly enhance FAQ completeness:

Concept Area	Questions	Impact	Difficulty
Quadrilaterals	9	High	Medium
Circle Concepts	9	High	Medium
Triangle Parts	6	Medium-High	Medium
Transformations	4	Medium	Medium

Total: 28 questions → Brings coverage to 91%

Nice-to-Have (Low Priority - 18 questions)

These complete the FAQ for advanced users:

Concept Area	Questions	Impact	Difficulty
Similarity	7	Medium	Medium-Hard
Advanced Right Triangles	4	Low-Medium	Hard
Trig Applications	3	Medium	Medium
3D Details	4	Low-Medium	Medium

Total: 18 questions → Brings coverage to 100%

Implementation Timeline

Week 1-2: Critical Triangle Content (12 questions)

Triangle congruence theorems (SSS, SAS, ASA, AAS, HL, CPCTC)
Triangle fundamental theorems (Sum, Exterior Angle, Triangle Inequality, Isosceles, Base Angles, Equilateral)

Week 3: Area and Volume (6 questions)

Basic area formulas (rectangle, triangle, circle)
Basic volume formulas (prism, cylinder, sphere)

Week 4: Triangle Centers and Terminology (6 questions)

Four triangle centers (centroid, incenter, circumcenter, orthocenter)
Detailed ray and vertex questions

Month 1 Complete: 24 critical questions added, 77% coverage

Month 2: Quadrilaterals (9 questions)

All major quadrilateral types and properties
Interior angle formulas

Month 3: Circles (9 questions)

Central and inscribed angles
Arc length and sectors
Tangent and chord properties

Month 4: Triangle Parts and Transformations (10 questions)

Medians, altitudes, bisectors
Detailed transformation procedures
Composition of transformations

Month 4 Complete: 52 questions added, 91% coverage

Month 5-6: Remaining Gaps (18 questions)

Similarity and proportions (7)
Advanced right triangle topics (4)
Trigonometry applications (3)
3D geometry details (4)

Month 6 Complete: 70 questions added, 100% coverage

Success Metrics

Completion Criteria

Phase 1 Success (Critical Gaps): - ✓ 24 new questions added - ✓ Coverage ≥ 75% - ✓ All triangle congruence theorems explained - ✓ Basic area/volume formulas included - ✓ Student can complete basic proofs

Phase 2 Success (Medium Priority): - ✓ 52 total new questions (24+28) - ✓ Coverage ≥ 90% - ✓ All polygon properties covered - ✓ Complete circle concept coverage - ✓ Student can solve all standard geometry problems

Phase 3 Success (Complete Coverage): - ✓ 70 total new questions (24+28+18) - ✓ Coverage = 100% - ✓ All 200 learning graph concepts addressed - ✓ Advanced topics explained - ✓ Student ready for advanced geometry or pre-calculus

Quality Standards for New Questions

Each new FAQ question should meet these criteria:

Answer Quality:
80-200 words (100-300 acceptable)
At least 60% should include examples
100% must have source links
Clear language for high school level
Bloom's Taxonomy:
Critical gaps: mostly Remember/Understand with some Apply
Medium priority: balanced Understand/Apply/Analyze
Low priority: more Analyze/Evaluate
Structure:
Clear, searchable question phrasing
Standalone answer (no external context required)
Links to relevant chapter sections
Examples for abstract concepts
Alignment:
Matches learning graph concept
Connects to existing FAQ questions where relevant
Uses consistent terminology from glossary

Conclusion

The current FAQ covers 130/200 concepts (65%) with excellent quality. Adding the recommended 70 questions in three phases will:

Phase 1 (24 questions): Close critical gaps → 77% coverage
Phase 2 (28 questions): Comprehensive coverage → 91% coverage
Phase 3 (18 questions): Complete coverage → 100% coverage

Highest Priority Actions: 1. Add triangle congruence theorem questions (SSS, SAS, ASA, AAS, HL, CPCTC) 2. Add triangle property theorem questions (Sum, Exterior Angle, Inequality) 3. Add basic area and volume formula questions 4. Add triangle center questions (centroid, incenter, circumcenter, orthocenter)

These additions will transform the FAQ from "good" (65% coverage) to "excellent" (77% coverage) and eventually to "comprehensive" (100% coverage), supporting students throughout their entire geometry journey.

Current Status: 65% concept coverage (130/200) Target Status: 100% concept coverage (200/200) Total Questions to Add: 70 (24 critical + 28 medium + 18 low priority) Timeline: 6 months for complete coverage Immediate Priority: 24 critical gap questions (brings to 77% coverage)