Question

I have finished half of this problem but i am still unsure on how to finish.

Answer 1

• ASA
• rigid

Explanation:

Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.

Sides and angles

The segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.

When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.

Motion

"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.

Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.

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Additional comment

The rigid motions include ...

• translation
• rotation
• reflection.

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Answer 2

Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.

Explanation:

For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.

For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.