Question

I need answers ASAP!!!

Jason states that Triangle A B C is congruent to triangle R S T. Kelley states that Triangle A B C is congruent to triangle T S R. Which best describes the accuracy of the congruency statements?

A) Jason’s statement is correct. RST is the same orientation, shape, and size as ABC.
B) Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a rotation and a translation of ABC.
C) Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.
D) Kelley’s statement is correct. TSR is the same orientation, shape, and size as ABC.

Answer 1

c

Explanation:

Answer 2

C) Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.

Explanation:

When naming congruent shapes, the orders of the congruent vertex letters need to be the same.

Since these are isosceles triangles, the base angles are the same:

m∠R = m∠T = m∠A = m∠C

Therefore the congruency statement can be written two different ways.

ΔABC ≅ ΔRST

ΔABC ≅ ΔTSR

Both statements could be correct.

Choosing between B) and C):

To move ΔABC to where ΔRST or ΔTSR is, you could either:

i) Translate 6 units to the left, and translate 3 units down

ii) Reflect across the y-axis, and translate 3 units down

It can be the result of two translations or a reflection and a translation.

In the result, the base side RT is on the bottom of the shape, like side AC. If you rotated the shape, the base side would not be on the bottom. Therefore B) is incorrect.