👩‍🏫 Teacher’s Guide

Objective
Recognize invalid congruence arguments such as SSA and AAA.

Teaching Notes

• Emphasize that congruent means same shape and size (stronger than similar).
• For triangle rules, highlight 'included' for SAS/ASA and right-triangle requirement for HL.
• Use CPCTC only after triangles are proven congruent.

🧒 Student Worksheet

Concept and Helping Material

These activities help you master Not a Valid Congruence Rule by identifying congruent figures and using triangle congruence rules and reasoning.

Math Vocabulary and Definition

• — side-angle-side, a triangle congruence rule using two sides and the included angle
• — side-side-side, a triangle congruence rule using three pairs of equal sides
• — angle-side-angle, a triangle congruence rule using two angles and the included side
• — angle-angle-side, a triangle congruence rule using two angles and a non-included side
• — hypotenuse-leg, a right-triangle congruence rule

Math Practics

1. AAA proves triangles are ______, not congruent.
2. SSA is generally ______ a valid triangle congruence rule.
3. Which is not a valid congruence rule: SSS, SAS, ASA, AAS, HL, or SSA?
4. Which is not a valid congruence rule: AAA or SSS?
5. Is SSA a valid triangle congruence rule? Answer Yes or No.
6. Is SSA a valid triangle congruence rule? Answer Yes or No.
7. Is SSA a valid triangle congruence rule? Answer Yes or No.
8. Is SSA a valid triangle congruence rule? Answer Yes or No.
9. Is SSA a valid triangle congruence rule? Answer Yes or No.
10. Is SSA a valid triangle congruence rule? Answer Yes or No.
11. Is SSA a valid triangle congruence rule? Answer Yes or No.
12. Is SSA a valid triangle congruence rule? Answer Yes or No.
13. Is SSA a valid triangle congruence rule? Answer Yes or No.
14. Is SSA a valid triangle congruence rule? Answer Yes or No.
15. Is SSA a valid triangle congruence rule? Answer Yes or No.
16. Is SSA a valid triangle congruence rule? Answer Yes or No.
17. Is SSA a valid triangle congruence rule? Answer Yes or No.
18. Is SSA a valid triangle congruence rule? Answer Yes or No.
19. Is SSA a valid triangle congruence rule? Answer Yes or No.
20. Is SSA a valid triangle congruence rule? Answer Yes or No.

Math Game

Reflection

• How did you decide which triangle congruence rule (SSS, SAS, ASA, AAS, HL) applied?

Guided extension: Congruence

Use after the core lesson. These questions revisit the topic as a whole; later skills can be assigned as an extension after their prerequisites.

Key idea

Congruent triangles have equal corresponding sides and angles. SSS, SAS, ASA, AAS, and HL (for right triangles) justify congruence. AAA establishes similarity; SSA is not a general congruence rule.

Worked example

Two triangles with sides 4,5,6 cm are congruent by SSS. Equal three angles alone would allow one triangle to be larger.

Explain and apply

1. Two triangles have equal sides 5 and 8 cm and equal included angle 40 degrees. Which rule applies?
2. Triangles have equal angles 35 and 65 degrees and equal included side. Which rule applies?
3. Two right triangles have equal hypotenuse and one equal leg. Which rule applies?
4. Why does AAA fail to prove congruence?

Teacher check

Ask students to show the setup, name any domain or unit restrictions, and explain a check of their answer. For extra support, complete the worked example together before revealing answers.

Source note

Source skill reference: Everything You Need to Ace Geometry in One.pdf, PDF pages 153-176. New examples and questions use original wording and values.