### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #574 : Geometry

; ; has perimeter 400.

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

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 #575 : Geometry

; ; has perimeter 300.

Evaluate .

**Possible Answers:**

Insufficient information is given to answer the problem.

**Correct answer:**

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:**

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 #577 : Geometry

.

Evaluate .

**Possible Answers:**

These triangles cannot exist.

**Correct answer:**

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

### Example Question #578 : Geometry

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.

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 #579 : Geometry

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

**Possible Answers:**

**Correct answer:**

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 #580 : Geometry

;

Which of the following is true about ?

**Possible Answers:**

is isosceles and obtuse.

is isosceles and acute.

is scalene and acute.

is scalene and obtuse.

None of the other responses is correct.

**Correct answer:**

is scalene and obtuse.

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 #1 : 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:**

Corresponding angles of similar triangles are congruent, so .

Consequently,

Therefore,

.

### 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:**

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

.

Order the triangles by perimeter, least to greatest.

**Possible Answers:**

**Correct answer:**

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

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