Looking at the worksheet, I need to determine which triangle congruence theorem applies to each pair of triangles based on the markings shown.
Let me go through each problem one by one:
Problem 1: Two triangles with two sides and the included angle marked as congruent. This matches the SAS (Side-Angle-Side) theorem.
Problem 2: Two right triangles with the hypotenuse and one leg marked as congruent. This is the HL (Hypotenuse-Leg) theorem for right triangles.
Problem 3: Two triangles with all three sides marked as congruent. This is the SSS (Side-Side-Side) theorem.
Problem 4: Two triangles with two angles and the included side marked as congruent. This is the ASA (Angle-Side-Angle) theorem.
Problem 5: Two right triangles with both legs marked as congruent. Since we have two sides and the included right angle, this is SAS.
Problem 6: Two triangles with two angles and a non-included side marked as congruent. This is the AAS (Angle-Angle-Side) theorem.
Problem 7: Two triangles with two sides and a non-included angle marked as congruent. This is SSA, which is not a valid congruence theorem, so the answer is "None".
Problem 8: Two right triangles with the hypotenuse and one leg marked as congruent. This is the HL theorem.
Problem 9: Two triangles with two angles and the included side marked as congruent. This is the ASA theorem.
Problem 10: Given AB ≅ CD and AD ≅ CB, we have two pairs of sides congruent. We also have AC as a common side, so all three sides are congruent. This is SSS.
Problem 11: Given ∠A ≅ ∠B, we only have one pair of angles congruent, which is not enough to prove congruence. So the answer is "None".
Problem 12: Given ∠ABE and ∠CDE, and AB ≅ CD. Looking at the diagram, we can see that ∠AEB and ∠CED are vertical angles (congruent), and we have AB ≅ CD. This gives us two angles and a non-included side, which is AAS.
Final Answer:
1. SAS
2. HL
3. SSS
4. ASA
5. SAS
6. AAS
7. None
8. HL
9. ASA
10. SSS
11. None
12. AAS
Parent Tip: Review the logic above to help your child master the concept of asa and aas congruence worksheet.
