Question

4520va v. geometry sem a geometry
triangle congruence: asa and aas
what are the rigid transformations that will map △abc to △def?
translate vertex b to vertex d, and then rotate
△abc around point b to align the sides and
angles.
translate vertex a to vertex d, and then rotate
△abc around point a to align the sides and
angles.
translate vertex b to vertex d, and then reflect
△abc across the line containing ac.
translate vertex a to vertex d, and then reflect
△abc across the line containing ac.

Explanation:

Step1: Analyze the vertices

We need to map \( \triangle ABC\) to \( \triangle DEF\). First, we consider translating vertex \(A\) to vertex \(D\) because they have the same angle (\(40^{\circ}\)) at those vertices.

Step2: Analyze the transformation type

After translating vertex \(A\) to vertex \(D\), we need to rotate \( \triangle ABC\) around point \(A\) (now at \(D\)) to align the sides and angles. Rotation is a rigid transformation that preserves shape and size, which is suitable for congruent triangles.

Answer:

Translate vertex \(A\) to vertex \(D\), and then rotate \( \triangle ABC\) around point \(A\) to align the sides and angles.