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SSAT Upper Level Math : Properties of Triangles

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Example Questions

Example Question #101 : Properties Of Triangles

Find the perimeter of a triangle with side lengths of 12, 12, 18 .

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a triangle, add up all of its sides.

$\text{Perimeter}=12+12+18=42$

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Example Question #102 : Properties Of Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Since the angle measurements in the base of the triangle are the same, this is an isosceles triangle. The side lengths directly across from the equal angles must be the same. Thus, the missing side length is .

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=5+5+3=13$

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Example Question #103 : Properties Of Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=16+16+18=50$

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Example Question #104 : Properties Of Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Since there are two angles that are the same, this is an isosceles triangle. The side lengths directly across from the equal angles must be the same. Thus, the missing side length is .

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=18+18+21=57$

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Example Question #105 : Properties Of Triangles

Find the perimeter of the triangle below:

Possible Answers:

Correct answer:

Explanation:

First, find the length of the missing side.

Since there are two angles that are the same, this is an isosceles triangle. The side lengths directly across from the equal angles must be the same. Thus, the missing side length is .

Now, to find the perimeter, add up all the side lengths.

$\text{Perimeter}=14+14+20=48$

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Example Question #106 : Properties Of Triangles

Triangle_a

Figure NOT drawn to scale.

If $x = 72^{\circ }$ and $y = 43^{\circ }$ , evaluate .

Possible Answers:

$65^{\circ}$

$137^{\circ}$

$108^{\circ}$

$115^{\circ }$

$125^{\circ }$

Correct answer:

$115^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$w = x + y = 72 + 43 = 115 ^{\circ }$

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Example Question #107 : Properties Of Triangles

If the vertex angle of an isoceles triangle is $64^{\circ}$ , what is the value of one of its base angles?

Possible Answers:

$36^{\circ}$

$116^{\circ}$

$58^{\circ}$

$64^{\circ}$

$26^{\circ}$

Correct answer:

$58^{\circ}$

Explanation:

In an isosceles triangle, the base angles are the same. Also, the three angles of a triangle add up to $180^{\circ}$ .

So, subtract the vertex angle from $180^{\circ}$ . You get $116^{\circ}$ .

Because there are two base angles you divide $116^{\circ}$ by , and you get $58^{\circ}$ .

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Example Question #108 : Properties Of Triangles

Triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram.

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Which of the following could be a measure of $\angle 3$ ?

Possible Answers:

$110^{\circ }$

$125^{\circ }$

$130^{\circ }$

All of the other choices give a possible measure of $\angle 3$ .

$100^{\circ }$

Correct answer:

$110^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$\angle 3 = \angle 1 + \angle 2$ .

We also have the following constraints:

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Then, by the addition property of inequalities,

$45^{\circ } + 60 ^{\circ }\leq m \angle 1 +m \angle 2 \leq 50^{\circ } + 70 ^{\circ }$

$105 ^{\circ }\leq m \angle 3 \leq 120^{\circ }$

Therefore, the measure of $\angle 3$ must fall in that range. Of the given choices, only $110^{\circ }$ falls in that range.

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Example Question #109 : Properties Of Triangles

Triangle

Refer to the above diagram.

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$130^{\circ } \leq m \angle 3 \leq 140 ^{\circ }$

Which of the following could be a measure of $\angle 2$ ?

Possible Answers:

$85 ^{\circ }$

$90 ^{\circ }$

$95 ^{\circ }$

$80 ^{\circ }$

All of the other responses are correct.

Correct answer:

All of the other responses are correct.

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$\angle 3 = \angle 1 + \angle 2$

$\angle 2 = \angle 3 - \angle 1$

Therefore, the maximum value of $\angle 2$ is the least possible value of $\angle 1$ subtracted from the greatest possible value of $\angle 3$ :

$140^{\circ } - 45^{\circ } = 95 ^{\circ }$

The minimum value of $\angle 2$ is the greatest possible value of $\angle 1$ subtracted from the least possible value of $\angle 3$ :

$130^{\circ } - 50^{\circ } = 80 ^{\circ }$

Therefore,

$80^{\circ } \leq \angle 2 \leq 95^{\circ }$

Since all of the choices fall in this range, all are possible measures of $\angle 2$ .

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Example Question #110 : Properties Of Triangles

Find the angle measurement of .

Possible Answers:

112

102

Correct answer:

102

Explanation:

All the angles in a triangle must add up to 180 .

32+46+y=180

78+y=180

y=102

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Properties of Triangles

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #101 : Properties Of Triangles

Example Question #102 : Properties Of Triangles

Example Question #103 : Properties Of Triangles

Example Question #104 : Properties Of Triangles

Example Question #105 : Properties Of Triangles

Example Question #106 : Properties Of Triangles

Example Question #107 : Properties Of Triangles

Example Question #108 : Properties Of Triangles

Example Question #109 : Properties Of Triangles

Example Question #110 : Properties Of Triangles

All SSAT Upper Level Math Resources

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