# GED Math : Similar Triangles and Proportions

## Example Questions

### Example Question #1 : Similar Triangles And Proportions

Which of the following statements is not a consequence of the statement

?

Explanation:

is simply a restatement of , since the names of the corresponding vertices of the similar triangles are still in the same relative positions.

is a consequence of , since corresponding angles of similar triangles are, by definition, congruent.

is a consequence of , since corresponding sides of similar triangles are, by definition, in proportion.

However, similar triangles need not have congruent corresponding sides. Therefore, it does not necessarily follow that . This is the correct choice.

### Example Question #2 : Similar Triangles And Proportions

Which of the following statements follows from the statement  ?

Explanation:

The similarity of two triangles implies nothing about the relationship of two angles of the same triangle. Therefore,  can be eliminated.

The similarity of two triangles implies that corresponding angles between the triangles are congruent. However, because of the positions of the letters,  in  corresponds to , not , in , so . The statement  can be eliminated.

Similarity of two triangles does not imply any congruence between sides of the triangles, so  can be eliminated.

Similarity of triangles implies that corresponding sides are in proportion.  and  in  correspond, respectively, to  and  in . Therefore, it follows that , and this statement is the correct choice.

### Example Question #3 : Similar Triangles And Proportions

Note: Figure NOT drawn to scale.

Refer to the above diagram. If , which of the following is false?

is a right angle

Explanation:

Suppose

Corresponding angles of similar triangles are congruent, so . Also, , so, since  is a right angle, so is .

Corresponding sides of similar triangles are in proportion. Since

the similarity ratio of  to  is 3.

By the Pythagorean Theorem, since  is the hypotenuse of a right triangle with legs 6 and 8, its measure is

.

, so  is a true statement.

But , so  is false if the triangles are similar. This is the correct choice.

### Example Question #4 : Similar Triangles And Proportions

Note: Figures NOT drawn to scale.

Refer to the above figures. Given that  , evaluate .

Explanation:

By the Pythagorean Theorem, since  is the hypotenuse of a right triangle with legs 6 and 8, its measure is

.

The similarity ratio of  to  is

.

Likewise,

### Example Question #5 : Similar Triangles And Proportions

Note: Figures NOT drawn to scale.

Refer to the above figures. Given that , give the area of .

Explanation:

Corresponding angles of similar triangles are congruent, so, since  is right, so is . This makes  and  the legs of a right triangle, so its area is half their product.

By the Pythagorean Theorem, since  is the hypotenuse of a right triangle with legs 6 and 8, its measure is

.

The similarity ratio of  to  is

.

This can be used to find  and :

The area of  is therefore

.

### Example Question #6 : Similar Triangles And Proportions

In the figure below, the two triangles are similar. Find the value of .