Question

the transformations given are performed on triangle abc to create triangle abc:

• (x,y)→(x + 10,y - 4)
• reflection across the x - axis

complete the sentence to explain whether or not the triangles are congruent.
triangle abc and abc are / are not congruent because each / neither / only the first transformation preserves side lengths and angle measures.
a. are / only the first
b. are not / neither
c. are / each
d. are not / each
e. are / neither

Explanation:

Step1: Analyze translation

The transformation $(x,y)\to(x + 10,y - 4)$ is a translation. Translations are rigid - motions that preserve side - lengths and angle - measures.

Step2: Analyze reflection

Reflection across the x - axis is also a rigid - motion. Rigid motions (translations, reflections, and rotations) preserve side - lengths and angle - measures.

Step3: Determine congruence

Since both the translation and the reflection are rigid motions, triangle ABC and A'B'C' are congruent because each transformation preserves side lengths and angle measures.

Answer:

C. are / each