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Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #121 : Acute / Obtuse Triangles

Sim._tri._vt_series

If the two triangles shown above are similar, what is the measurements for angles and ?

Possible Answers:

$a=75^\circ$ , $b=30^\circ$

$a=130^\circ$ , $b=30^\circ$

Not enough information is provided.

$a=37.5^\circ$ , $b=15^\circ$

Correct answer:

$a=75^\circ$ , $b=30^\circ$

Explanation:

In order for two triangles to be similar, they must have equivalent interior angles.

Thus, angle a=75 degrees and angle b=30 degrees.

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Example Question #122 : Acute / Obtuse Triangles

Sim._tri._vt_series

Using the similar triangles above, find a possible measurement for sides and .

Possible Answers:

y=6 and x=16

y=3 and x=9

y=8 and x=16

y=8 and x=18

Correct answer:

y=6 and x=16

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The original ratio of side lengths is:

3:8

Thus a similar triangle will have this same ratio:

$3:8\rightarrow 3\cdot 2:8\cdot2\rightarrow 6:16$

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

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths and . What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

and

Correct answer:

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of side lengths for triangle one is:

5:7

Thus the ratio of side lengths for the second triangle must following this as well:

$5:7\rightarrow 5\cdot 3: 7\cdot 3=15:21$ , because both side lengths in triangle one have been multiplied by a factor of .

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Example Question #124 : Acute / Obtuse Triangles

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths and . What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

and

Correct answer:

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of triangle one is:

$6:2\rightarrow 3:1$

Therefore, looking at the possible solutions we see that one answer has the same ratio as triangle one.

$3\cdot 8: 1\cdot 8 \rightarrow 24:8=3:1$

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

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths and . What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

and

Correct answer:

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of the side lengths in triangle one is:

16:9

If we take this ratio and look at the possible solutions we will see:

$16:9=(16\times 2):(9\times 2)$

16:9=32:18

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

Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths mm and mm. What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

92mm and 140mm

13mm and 17mm

21mm and 32mm

46mm and 65mm

Correct answer:

92mm and 140mm

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of triangle one is:

23:35

If we look at the possible solutions we will see that ratio that is in triangle one is also seen in the triangle with side lengths as follows:

$23:35=(23\times 4):(35\times 4)=92:140$

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Example Question #182 : Triangles

Tri_sim_vt_series_cont_

Using the triangle shown above, find possible measurements for the corresponding sides of a similar triangle?

Possible Answers:

and

Correct answer:

and

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of the triangle is:

7:16

Applying this ratio we are able to find the lengths of a similar triangle.

$7:16=(7\times 3):(16\times3)=21:48$

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Example Question #121 : Acute / Obtuse Triangles

Tri_sim_vt_series_cont_

Using the triangle shown above, find possible measurements for the corresponding sides of a similar triangle?

Possible Answers:

and

145 and 165

200 and 213

Correct answer:

145 and 165

Explanation:

Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.

The ratio of the triangle is:

29:33

Applying this ratio we are able to find the lengths of a similar triangle.

$29:33=(29\times 5):(33\times 5)=145:165$

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Example Question #181 : Triangles

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ .

AB = 10

BC = 15

DE = 12

EF = 18

$m\angle B = 78 ^{\circ }$

$m\angle E = 78 ^{\circ }$

True or false: It follows from the given information that $\bigtriangleup ABC \sim \bigtriangleup DEF$ .

Possible Answers:

False

True

Correct answer:

True

Explanation:

As we are establishing whether or not $\bigtriangleup ABC \sim \bigtriangleup DEF$ , then , , and correspond respectively to , , and .

According to the Side-Angle-Side Similarity Theorem (SASS), if the lengths of two pairs of corresponding sides of two triangles are in proportion, and their included angles are congruent, then the triangles are similar.

$\overline{AB}$ and $\overline{DE}$ are corresponding sides, as are $\overline{BC}$ and $\overline{EF}$ ; $\angle B$ and $\angle E$ are their included angles. Substituting

$\frac{AB}{DE} = \frac{10}{12}= \frac{5}{6}$

$\frac{BC}{EF} = \frac{15}{18} = \frac{5}{6}$

Therefore, $\frac{AB}{DE} =\frac{BC}{EF}$ , and corresponding sides are in proportion.

$m \angle B = 78^{\circ }$ and $m \angle E = 78^{\circ }$ ; the included angles are congruent.

The conditions of SASS are met, and it follows that $\bigtriangleup ABC \sim \bigtriangleup DEF$ .

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Example Question #631 : Intermediate Geometry

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ .

A B = 12

AC = 18

BC = 24

DE = 18

DF = 24

EF = 30

True or false: From the above six statements, it follows that $\bigtriangleup ABC \sim \bigtriangleup DEF$ .

Possible Answers:

False

True

Correct answer:

False

Explanation:

As we are establishing whether or not $\bigtriangleup ABC \sim \bigtriangleup DEF$ , then , , and correspond respectively to , , and .

If $\bigtriangleup ABC \sim \bigtriangleup DEF$ , then corresponding sides must be in proportion; that is, it must hold that

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

Substituting the lengths of the sides for the respective quantities:

A B = 12

AC = 18

BC = 24

DE = 18

DF = 24

EF = 30

$\frac{AB}{DE} = \frac{12}{18} = \frac{2}{3}$

$\frac{AC}{DF} = \frac{18}{30} = \frac{3}{5}$

The inequality of these two side ratios disproves the similarity of the triangles, so the correct answer is "false".

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Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #121 : Acute / Obtuse Triangles

Example Question #122 : Acute / Obtuse Triangles

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

Example Question #124 : Acute / Obtuse Triangles

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

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

Example Question #182 : Triangles

Example Question #121 : Acute / Obtuse Triangles

Example Question #181 : Triangles

Example Question #631 : Intermediate Geometry

All Intermediate Geometry Resources

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