Congruent Triangles Notes and Worksheets - Lindsay Bowden - Free Printable

Problem Analysis

The task involves determining whether pairs of triangles are congruent using the criteria SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg for right triangles). If the triangles are not congruent, the answer is "no." For questions 10-12, we need to complete the congruency statements.

Solution

#### 1.
- Triangles: Two right triangles with marked legs and hypotenuses.
- Analysis: Both triangles have two legs marked as equal and a right angle between them. This satisfies the SAS criterion.
- Answer: SAS

#### 2.
- Triangles: Two triangles with marked sides and angles.
- Analysis: The triangles have two sides and the included angle marked as equal. This satisfies the SAS criterion.
- Answer: SAS

#### 3.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: This satisfies the HL (Hypotenuse-Leg) criterion for right triangles.
- Answer: HL

#### 4.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: This satisfies the HL criterion for right triangles.
- Answer: HL

#### 5.
- Triangles: Two triangles with all three sides marked as equal.
- Analysis: This satisfies the SSS criterion.
- Answer: SSS

#### 6.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: This satisfies the HL criterion for right triangles.
- Answer: HL

#### 7.
- Triangles: Two triangles with two angles and a non-included side marked as equal.
- Analysis: This satisfies the AAS criterion.
- Answer: AAS

#### 8.
- Triangles: Two triangles with all three sides marked as equal.
- Analysis: This satisfies the SSS criterion.
- Answer: SSS

#### 9.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: This satisfies the HL criterion for right triangles.
- Answer: HL

#### 10.
- Triangles: ΔBCA and another triangle in the diagram.
- Analysis: The triangle ΔBCA is congruent to ΔECD by SSS (all three sides are marked as equal).
- Answer: ECD

#### 11.
- Triangles: ΔJLK and another triangle in the diagram.
- Analysis: The triangle ΔJLK is congruent to ΔMKH by ASA (two angles and the included side are marked as equal).
- Answer: MKH

#### 12.
- Triangles: ΔQTR and another triangle in the diagram.
- Analysis: The triangle ΔQTR is congruent to ΔRSQ by SAS (two sides and the included angle are marked as equal).
- Answer: RSQ

Final Answers

1. SAS
2. SAS
3. HL
4. HL
5. SSS
6. HL
7. AAS
8. SSS
9. HL
10. ECD
11. MKH
12. RSQ

Boxed Final Answer:
\[
\boxed{\text{SAS, SAS, HL, HL, SSS, HL, AAS, SSS, HL, ECD, MKH, RSQ}}
\]