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 a right angle, and the corresponding legs and hypotenuses are marked as equal.
- Conclusion: The triangles are congruent by HL (Hypotenuse-Leg).

#### 2.
- Triangles: Two triangles with marked sides and angles.
- Analysis: The triangles have two pairs of corresponding sides marked as equal, and the included angles are also marked as equal.
- Conclusion: The triangles are congruent by SAS (Side-Angle-Side).

#### 3.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: Both triangles have a right angle, and one leg and the hypotenuse are marked as equal.
- Conclusion: The triangles are congruent by HL (Hypotenuse-Leg).

#### 4.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: Both triangles have a right angle, and one leg and the hypotenuse are marked as equal.
- Conclusion: The triangles are congruent by HL (Hypotenuse-Leg).

#### 5.
- Triangles: Two triangles with all three sides marked as equal.
- Analysis: All three sides of the triangles are marked as equal.
- Conclusion: The triangles are congruent by SSS (Side-Side-Side).

#### 6.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: Both triangles have a right angle, and one leg and the hypotenuse are marked as equal.
- Conclusion: The triangles are congruent by HL (Hypotenuse-Leg).

#### 7.
- Triangles: Two triangles with two angles and a non-included side marked as equal.
- Analysis: Two angles and a non-included side are marked as equal.
- Conclusion: The triangles are congruent by AAS (Angle-Angle-Side).

#### 8.
- Triangles: Two triangles with all three sides marked as equal.
- Analysis: All three sides of the triangles are marked as equal.
- Conclusion: The triangles are congruent by SSS (Side-Side-Side).

#### 9.
- Triangles: Two right triangles with one leg and the hypotenuse marked as equal.
- Analysis: Both triangles have a right angle, and one leg and the hypotenuse are marked as equal.
- Conclusion: The triangles are congruent by HL (Hypotenuse-Leg).

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

#### 11.
- Triangles: ΔJLK and another triangle in the diagram.
- Analysis: The diagram shows that ΔJLK is congruent to ΔMKH by SAS (two sides and the included angle are marked as equal).
- Conclusion: ΔJLK ≅ ΔMKH.

#### 12.
- Triangles: ΔQTR and another triangle in the diagram.
- Analysis: The diagram shows that ΔQTR is congruent to ΔSRP by ASA (two angles and the included side are marked as equal).
- Conclusion: ΔQTR ≅ ΔSRP.

Final Answers

1. HL
2. SAS
3. HL
4. HL
5. SSS
6. HL
7. AAS
8. SSS
9. HL
10. ΔECD
11. ΔMKH
12. ΔSRP

\boxed{HL, SAS, HL, HL, SSS, HL, AAS, SSS, HL, \Delta ECD, \Delta MKH, \Delta SRP}