Question

a rotation and reflection are applied to △abc to create △dep. the rotation is 90° about the origin and the reflection is across the y - axis. is △abc congruent to △dep? use the drop - down menus to explain your response. click the arrow to choose an answer from each menu. of rotations and reflections, choose... can be used to transform a triangle into a congruent triangle. the corresponding sides of △abc and △def are choose... . the corresponding angles of △abc and △def are choose... . therefore △abc and △def are choose... .

Explanation:

Step1: Recall transformation properties

Rotations and reflections are rigid - motions. Rigid - motions preserve the shape and size of a figure.

Step2: Analyze side - length and angle - measure preservation

Since rotations and reflections are rigid - motions, the corresponding sides of two triangles formed by these transformations are congruent and the corresponding angles are congruent.

Step3: Determine triangle congruence

If the corresponding sides and angles of two triangles are congruent, the triangles are congruent.

Answer:

Of rotations and reflections, both can be used to transform a triangle into a congruent triangle. The corresponding sides of $\triangle ABC$ and $\triangle DEF$ are congruent. The corresponding angles of $\triangle ABC$ and $\triangle DEF$ are congruent. Therefore $\triangle ABC$ and $\triangle DEF$ are congruent.