Question

What two transformations need to be perfomed to show that the triangles are congruent?





(2 points)
Responses
which two answers are correct and why

Reflection
Reflection

Dilation
Dilation

Rotation
Rotation

Translation
Translation
Question 2
What congruency theorem does this justify?(1 point)
Responses

AAS
AAS

AAA
AAA

ASA
ASA

SSS
SSS

HL
HL
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Answer 1

To determine the congruency of triangles through transformations, we typically consider the types of movements required to manipulate one triangle to match another.

### Question 1:
For the two transformations required to show that the triangles are congruent:

1. **Reflection**
2. **Translation**

These transformations can be sufficient to ensure that one triangle aligns perfectly with the other, considering that reflection flips the triangle over a line (producing a mirror image), and a translation shifts it to the correct position.

### Question 2:
For the congruency theorem justifying the transformation, the correct answer would likely be:

- **AAS (Angle-Angle-Side)**

This is typically justified if the two angles and the included side (or the non-included side) are preserved or confirmed through the transformation process. The reflection and translation adjustment show the necessary congruencies in angles and sides, supporting the AAS theorem.

**Summary of Answers:**
1. Transformations: Reflection and Translation
2. Congruency theorem: AAS