Question

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Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

Answer 1

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Answer is  A

Answer 2

Answer: The correct option is 1.

Explanation:

From the given figure it is noticed that there are two right angle triangles.

In triangle RST and triangle VUT the angle S and U are same.

$\frac{RS}{VU} =\frac{12}{6} =2$

$\frac{ST}{UT}= \frac{16}{8}=2$

The ratio of the sides are same and an angle is congruent, therefore by SAS the triangle SAS both triangles are similar.

The option 2 and 4 contains the ratio of three sides but only two sides of each triangle are known so option 2 and 4 is incorrect.

$\frac{RS}{VU} =\frac{12}{6} =2$

$\frac{TU}{TS}= \frac{8}{16}=\frac{1}{2}$

$\frac{RS}{VU}\neq \frac{TU}{TS}$

So, the option 3 is incorrect.