SSAT Upper Level Math : How to find if two acute / obtuse triangles are similar

Study concepts, example questions & explanations for SSAT Upper Level Math

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

 has perimeter 400.

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

The perimeter of  is actually irrelevant to this problem. Corresponding sides of similar triangles are in proportion, so use this to calculate , or :

 

 

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

 has perimeter 300.

Evaluate .

Possible Answers:

Insufficient information is given to answer the problem.

Correct answer:

Explanation:

The ratio of the perimeters of two similar triangles is equal to the ratio of the lengths of a pair of corresponding sides. Therefore, 

 and , or

By one of the properties of proportions, it follows that

The perimeter of  is

, so

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

 has perimeter 90.

Give the perimeter of .

Possible Answers:

Correct answer:

Explanation:

The ratio of the perimeters of two similar triangles is the same as the ratio of the lengths of a pair of corresponding sides. Therefore, 

Example Question #4 : How To Find If Two Acute / Obtuse Triangles Are Similar

.

Evaluate .

Possible Answers:

These triangles cannot exist.

Correct answer:

Explanation:

The similarity of the triangles is actually extraneous information here. The sum of the measures of a triangle is , so:

Example Question #5 : How To Find If Two Acute / Obtuse Triangles Are Similar

Given:  and  and .

Which of the following statements would not be enough, along with what is given, to prove that ?

Possible Answers:

The given information is enough to prove the triangles similar.

Correct answer:

The given information is enough to prove the triangles similar.

Explanation:

Two pairs of corresponding angles are stated to be congruent in the main body of the problem; it follows from the Angle-Angle Similarity Postulate that the triangles are similar. No further information is needed.

Example Question #6 : How To Find If Two Acute / Obtuse Triangles Are Similar

. Which of the following is the ratio of the area of  to that of  ?

Possible Answers:

Correct answer:

Explanation:

 The similarity ratio of  to  is equal to the ratio of two corresponding sidelengths, which is given as ; the similarity ratio of  to  is the reciprocal of this, or .

The ratio of the area of a figure to that of one to which it is similar is the square of the similarity ratio, so the ratio of the area of  to that of  is 

Example Question #7 : How To Find If Two Acute / Obtuse Triangles Are Similar

 

Which of the following is true about ?

Possible Answers:

 is scalene and acute.

 is isosceles and acute.

 is isosceles and obtuse.

 is scalene and obtuse.

None of the other responses is correct.

Correct answer:

 is scalene and obtuse.

Explanation:

Corresponding angles of similar triangles are congruent, so the measures of the angles of  are equal to those of .

Two of the angles of  have measures  and ; its third angle measures 

.

One of the angles having measure greater than  makes  - and, consequently,  - an obtuse triangle. Also, the three angles have different measures, so the sides do as well, making  scalene.

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

.

Which of the following correctly gives the relationship of the angles of  ?

Possible Answers:

Correct answer:

Explanation:

Corresponding angles of similar triangles are congruent, so .

Consequently, 

Therefore,

.

Example Question #3 : How To Find If Two Acute / Obtuse Triangles Are Similar

Which of the following correctly gives the relationship of the angles of 

Possible Answers:

Correct answer:

Explanation:

Corresponding sides of similar triangles are in proportion; since ,

Therefore, 

The angle opposite the longest (shortest) side of a triangle is the angle of greatest (least) measure, so

.

Example Question #10 : How To Find If Two Acute / Obtuse Triangles Are Similar

.

Order the triangles by perimeter, least to greatest.

Possible Answers:

Correct answer:

Explanation:

 and  are corresponding sides of their respective triangles, and , so it easily follows from proportionality that each side of  is shorter than its corresponding side in . Therefore,  is of lesser perimeter than . By the same reasoning, since ,   is of lesser perimeter than .

The correct response is

← Previous 1
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: