Question

which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?​

Answer 1

Answer:

B

Step-by-step explanation:

You are given two right triangles PQR and XYZ with PQ=12, PR=6, XY=4, XZ=2. Note that

$\dfrac{PQ}{XY}=\dfrac{12}{4}=3\Rightarrow PQ=3XY\\ \\\dfrac{PR}{XZ}=\dfrac{6}{2}=3\Rightarrow PR=3XZ$

So, in these triangles:

• ∠P=∠X=90°;
• PQ=3XY;
• PR=3XZ.

Hence, by SAS theorem these triangles are similar.

SAS Similarity Theorem states that given two triangles are similar if their two sides are in proportion and their angles adjacent to these sides  have the same measure.