Question

What similarity statement can you write relating the three triangles in the diagram?

Answer 1

Answer choices:

A. EAK ~ GAK ~EGA
B. EAK ~ AGK ~ EAG
C. EKA ~ AGK ~ EGA
D. EAK ~ AGK ~ EGA

Answer 2

First, let's see which angles are corresponding angles.
All triangles are right triangles.
Can you name the three right angles?

Answer 3

EAK, EGA, and AGK

Answer 4

I think i'm not positive, im very tired

Answer 5

You are correct. That was great.

Answer 6

Since when naming a triangle, only the middle letter of the angle is used, then you know that the letters A, G, and G have to correspond to each other.

Answer 7

Go through each choice, and see which one has A, G, and G as corresponding vertices.

Answer 8

corresponding would mean that that letter is in the middle right?

Answer 9

No. In the naming of the triangles, corresponding angles or vertices means the letter is in the same position. They are all in the middle, or all the first letter, or all the last letter.

Answer 10

\(\sf A. ~~~\triangle E\color{red}{A}K \sim~ \triangle \color{red}{G}AK \sim~ \triangle E\color{red}{G}A \)
\(\sf B. ~~~\triangle EAK \sim~ \triangle AGK \sim~ \triangle EAG \)
\(\sf C. ~~~\triangle EKA \sim~ \triangle AGK \sim~ \triangle EGA \)
\(\sf D.~~~ \triangle EAK \sim~ \triangle AGK \sim~ \triangle EGA \)

Answer 11

Look at the choices above.
Notice choice A.
The vertices of the right angles for each triangle are in red.
The three triangles named are indeed the three triangles in the figure.
The right angles must be in the same position in each choice.
In triangle EAK, the right angle is A, and it is in the middle.
In triangles GAK and EGA, the right angle is G. That means G would also have to be in the middle. In choice A, the three right angles are not in the same position in all three triangles, so choice A is incorrect.

Answer 12

Thank you, that helped a lot.

Answer 13

Now do the same for the other choices.

Answer 14

Well I think it's D, but it might be wrong

Answer 15

\(\sf A. ~~~\triangle E\color{red}{A}K \sim~ \triangle \color{red}{G}AK \sim~ \triangle E\color{red}{G}A \)
\(\sf B. ~~~\triangle EAK \sim~ \triangle AGK \sim~ \triangle EAG \)
\(\sf C. ~~~\triangle EKA \sim~ \triangle AGK \sim~ \triangle EGA \)
\(\sf D.~~~ \triangle E\color{red}{A}K \sim~ \triangle A\color{red}{G}K \sim~ \triangle E\color{red}{G}A \)

Answer 16

This is the only choice in which all three right angles are corresponding, so it has to be the correct choice.

Answer 17

ok, thanks again!(:

Answer 18

You're welcome.