Question

In the triangle below, chord RT is parallel to chord HS.

What is the value of x?

Answer 1

Given chord RT is parallel to chord HS, can you tell which two triangles in the figure must be similar?

Answer 2

Triangle MRT and triangle MHS

Answer 3

Right! By which postulate?

Answer 4

SSS?

Answer 5

No. SSS is a postulate of congruence not similarity. Any other ideas? How are the two triangles similar?

Answer 6

I'm not sure. But they're similar because of the chords..

Answer 7

The two triangles MRT and MHS are similar because of equal angles, that is, due to the AA postulate. Since chords are parallel so their corresponding angles are equal on both sides. So AA postulate

Answer 8

Oh okay

Answer 9

Form a ratio and proportion involving the sides of the similar triangles. Ratios of sides of similar triangles are equal.

Answer 10

\[\frac{ 6 }{ 4 }=\frac{ 15 }{ x }\]

Answer 11

x=10

Answer 12

No. 6 and 15 can't be in the ratio since they are not the side lengths of a particular triangle. They are just parts of the side lengths. For similar triangles, the ratio of their total side lengths is equal to each other.

Answer 13

But my answer key says the answer is 10 and when you use cross products you get 10...

Answer 14

The answer is x = 10 even if you solve it the incorrect way as you have done above. The correct proportion is \[x/(x + 15)=4/10\]However you will not get the correct answer from the proportion you made above in all questions.

Answer 15

Ohh okay I see what I did wrong. Thank you!