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SSAT Upper Level Math : Geometry

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #591 : Geometry

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ ; $\frac{AB}{DE} = \frac{AC}{DF}$ .

Which of the following statements would not be enough, along with what is given, to prove that $\bigtriangleup ABC \sim \bigtriangleup DEF$ ?

Possible Answers:

$\angle A \cong \angle D$

$\angle C \cong \angle F$

$\frac{AC}{DF}= \frac{BC}{EF}$

The given information is enough to prove the triangles similar.

$\frac{AB}{DE} = \frac{BC}{EF}$

Correct answer:

$\angle C \cong \angle F$

Explanation:

From both the given proportion statement and either $\frac{AB}{DE} = \frac{BC}{EF}$ or $\frac{AC}{DF}= \frac{BC}{EF}$ , it follows that $\frac{AB}{DE} =\frac{AC}{DF}= \frac{BC}{EF}$ —all three pairs of corresponding sides are in proportion; by the Side-Side-Side Similarity Theorem, $\bigtriangleup ABC \sim \bigtriangleup DEF$ . From the given proportion statement and $\angle A \cong \angle D$ , since these are the included angles of the sides that are in proportion, then by the Side-Angle-Side Similarity Theorem, $\bigtriangleup ABC \sim \bigtriangleup DEF$ . From the given proportion statement and $\angle C \cong \angle F$ , since these are nonincluded angles of the sides that are in proportion, no similarity can be deduced.

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

The area of a triangle is 240 , and the base of the triangle is . What is the height for this triangle?

Possible Answers:

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$240=\frac{30 \times h}{2}$

480=30h

h=16

The height of the triangle is .

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 360m^2 and a base of 60m . In meters, find the height.

Possible Answers:

12m

24m

18m

Correct answer:

12m

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$360=\frac{60\times h}{2}$

720=60h

h=12

The height of the triangle is meters.

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Example Question #61 : Acute / Obtuse Triangles

A triangle has an area of and a base of . Find the height.

Possible Answers:

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$45=\frac{15\times h}{2}$

90=15h

h=6

The height of the triangle is .

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of and a base of . Find the height.

Possible Answers:

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$24=\frac{12\times h}{2}$

48=12h

h=4

The height of the triangle is .

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Example Question #153 : Properties Of Triangles

A triangle has an area of and a base of . Find the height.

Possible Answers:

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$54=\frac{12\times h}{2}$

108=12h

h=9

The height of the triangle is .

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Example Question #154 : Properties Of Triangles

A triangle has an area of and a base of . Find the height.

Possible Answers:

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$60=\frac{12\times h}{2}$

120=12h

h=10

The height of the triangle is .

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Example Question #2 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 24x^2 and a base of . In terms of , find the height.

Possible Answers:

10x

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$24x^2=\frac{6x\times h}{2}$

48x^2=6x(h)

$h=\frac{48x^2}{6x}=8x$

The height of the triangle is .

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Example Question #151 : Properties Of Triangles

A triangle has an area of 128y^2 and a base of 16y . In terms of , find the height.

Possible Answers:

16y

12y

20y

Correct answer:

16y

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$128y^2=\frac{16y\times h}{2}$

256y^2=16y(h)

h=16y

The height of the triangle is 16y .

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Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

A triangle has an area of 48a and a base of . What is the height?

Possible Answers:

16a

Correct answer:

Explanation:

Use the formula to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Now, plug in the values for the area and the base to solve for height .

$48a=\frac{6a\times h}{2}$

96a=6a(h)

$h=\frac{96a}{6a}=\frac{96}{6}=16$

The height of the triangle is .

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #591 : Geometry

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #61 : Acute / Obtuse Triangles

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #153 : Properties Of Triangles

Example Question #154 : Properties Of Triangles

Example Question #2 : How To Find The Height Of An Acute / Obtuse Triangle

Example Question #151 : Properties Of Triangles

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

All SSAT Upper Level Math Resources

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