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; TSU ~ PJM

Explanation:

Because the angle in between the sides are the same, we can see if each corresponding side is proportional to each other. If they are, then they are similar. (This is SAS similarity theorem)

First we can divide 10 by 15 and see if 14 divided by 21 is the same:

10/15 = 0.6666....

14/21 = 0.6666....

Yes, the two triangles are similar

Answer 2

Δ STU
`\bold{\sim}` ΔPJM similar

Explanation:

Similar triangles are two or more triangles that have the same shape, but their sides are in proportion. In other words, if you divide the length of any side of one triangle by the corresponding side of another triangle, you will get the same number.

For Question:

In Δ STU and ΔPJM

TS:US =10:14=5:7

PJ: JM=15:21= 5:7

Since the length of any side of one triangle is by the corresponding side of another triangle, you will get the same number.

Therefore,

Δ STU
`\bold{\sim}` ΔPJM is similar.

Hence Proved: