7
Prove: ARUN ~ ACAT
R
8.2
47
16.4
8.4
103°
T
U
N
122

I'm assuming point U is in the bottom left corner of the larger triangle, and point N is in the bottom right corner.

If so, then that makes segment RU = 8.4 and we can see that CA = 4.2

Note how RU/CA = (8.4)/(4.2) = 2

Also, note that RN/CT = (16.4)/(8.2) = 2

Both ratios lead to the result of 2, meaning that segments of triangle RUN are twice as long compared to the corresponding segments of triangle CAT. Put another way, the sides are in the same ratio or proportion.

This fact, coupled with the fact that angle R = angle C = 47, will allow us to use the SAS similarity theorem to prove triangle RUN is similar to triangle CAT.

10cm

step-by-step explanation:

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