GED Math : Similar Triangles and Proportions

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #258 : Geometry And Graphs

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

 ?

Possible Answers:

Correct answer:

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 #81 : Triangles

Which of the following statements follows from the statement  ?

Possible Answers:

Correct answer:

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 #82 : Triangles

Triangles

Note: Figure NOT drawn to scale.

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

Possible Answers:

 is a right angle

Correct answer:

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 #1 : Similar Triangles And Proportions

Triangles

Note: Figures NOT drawn to scale.

Refer to the above figures. Given that  , evaluate .

Possible Answers:

Correct answer:

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 #2 : Similar Triangles And Proportions

Triangles

Note: Figures NOT drawn to scale.

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

Possible Answers:

Correct answer:

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 #3 : Similar Triangles And Proportions

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

2

Possible Answers:

Correct answer:

Explanation:

Since the two triangles are similar, we know that their corresponding sides must be in the same ratio to each other. Thus, we can write the following equation:

Now, solve for .

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