Question

100 Points! Geometry question. Determine whether each pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Photo attached. Thank you!

Answer 1

Yes, the triangle are similar.

Explanation:

To prove that 2 triangle are similar you only need to prove that 2 corresponding angles are equal.

The sum of the interior angles add to 180.

< m on the left measures 30 degrees.

80 - 90 - 60 = 30

> t on the right measures 60 degrees.

180 - 90 - 30 = 60

If two corresponding angles of two triangles are equal that forces the third pair to be congruent, since the total of the angles must add up to 180.

Although we are not given the corresponding sides, there are proportional because the angles are equal.

Helping in the name of Jesus.

Answer 2

Similar triangles are triangles that have the same shape but different sizes. In other words, if two triangles are similar, then their corresponding angles are congruent and their corresponding sides are in equal proportion.

For Question:

In Δ MSK and ΔQRT

∡S=∡R right angle

∡K=∡T=180°-90°-30°=60° Given

∡M=∡Q=180°-90°-60°=30° Given

Therefore,

Δ MSK
`\bold{\sim}` ΔQRT

By AA similarity.

Hence Proved: