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Intermediate Geometry : Plane Geometry

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Example Questions

Example Question #621 : Plane Geometry

Are the two triangles similar? If so, which postulate proves their similarity? (Figure not drawn to scale)

Possible Answers:

Yes, side-side-side postulate

No, the triangles are not equal

Yes, angle-angle postulate

Yes, side-angle-side postulate

Correct answer:

Yes, angle-angle postulate

Explanation:

The triangles are similar by the angle-angle postulate. 2 corresponding angles are equal to each other, therefore, the triangles must be similar.

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Example Question #622 : Plane Geometry

Are the two triangles similar? If so, which postulate proves their similarity? (Figure not drawn to scale)

Possible Answers:

Yes; angle-angle postulate

Yes; side-angle-side postulate

Yes; side-side-side postulate

No, the triangles are not similar

Correct answer:

No, the triangles are not similar

Explanation:

The triangles are not similar, and it can be proven through the side-angle-side postulate. The SAS postulate states that two sides flanking a corresponding angle must be similar. In this case, the angles are congruent. However, the sides are not similar.

$\frac{12}{3}=4$ $\displaystyle \frac{12}{3}=4$

$\frac{18}{4}=4.5$ $\displaystyle \frac{18}{4}=4.5$

$4.5 \neq 4$ $\displaystyle 4.5 \neq 4$

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Example Question #121 : Acute / Obtuse Triangles

Sim._tri._vt_series

If the two triangles shown above are similar, what is the measurements for angles $\displaystyle a$ and $\displaystyle b$ ?

Possible Answers:

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

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

Not enough information is provided.

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

Correct answer:

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

Explanation:

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

Thus, angle a=75 $\displaystyle a=75$ degrees and angle b=30 $\displaystyle b=30$ 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 $\displaystyle x$ and $\displaystyle y$ .

Possible Answers:

y=6 $\displaystyle y=6$ and x=16 $\displaystyle x=16$

y=3 $\displaystyle y=3$ and x=9 $\displaystyle x=9$

y=8 $\displaystyle y=8$ and x=16 $\displaystyle x=16$

y=8 $\displaystyle y=8$ and x=18 $\displaystyle x=18$

Correct answer:

y=6 $\displaystyle y=6$ and x=16 $\displaystyle x=16$

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 $\displaystyle 3:8$

Thus a similar triangle will have this same ratio:

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

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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 $\displaystyle 5$ and $\displaystyle 7$ . What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

$\displaystyle 15$ and $\displaystyle 17$

$\displaystyle 4$ and $\displaystyle 6$

$\displaystyle 15$ and $\displaystyle 21$

$\displaystyle 9$ and $\displaystyle 12$

Correct answer:

$\displaystyle 15$ and $\displaystyle 21$

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 $\displaystyle 5:7$

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

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

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Example Question #3 : 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 $\displaystyle 6$ and $\displaystyle 2$ . What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

$\displaystyle 4$ and $\displaystyle 1$

$\displaystyle 1$ and $\displaystyle 4$

$\displaystyle 18$ and $\displaystyle 8$

$\displaystyle 24$ and $\displaystyle 8$

Correct answer:

$\displaystyle 24$ and $\displaystyle 8$

Explanation:

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

The ratio of triangle one is:

$6:2\rightarrow 3:1$ $\displaystyle 6:2\rightarrow 3:1$

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

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

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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 $\displaystyle 16$ and $\displaystyle 9$ . What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

$\displaystyle 21$ and $\displaystyle 34$

$\displaystyle 34$ and $\displaystyle 18$

$\displaystyle 34$ and $\displaystyle 21$

$\displaystyle 32$ and $\displaystyle 18$

Correct answer:

$\displaystyle 32$ and $\displaystyle 18$

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 $\displaystyle 16:9$

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

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

$\displaystyle 16:9=32:18$

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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 $\displaystyle 23$ mm and $\displaystyle 35$ mm. What are possible measurements for the corresponding sides in triangle two?

Possible Answers:

92mm $\displaystyle 92mm$ and 140mm $\displaystyle 140mm$

13mm $\displaystyle 13mm$ and 17mm $\displaystyle 17mm$

21mm $\displaystyle 21mm$ and 32mm $\displaystyle 32mm$

46mm $\displaystyle 46mm$ and 65mm $\displaystyle 65mm$

Correct answer:

92mm $\displaystyle 92mm$ and 140mm $\displaystyle 140mm$

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 $\displaystyle 23:35$

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:

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

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

Tri_sim_vt_series_cont_

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

Possible Answers:

$\displaystyle 3$ and $\displaystyle 7$

$\displaystyle 23$ and $\displaystyle 46$

$\displaystyle 5$ and $\displaystyle 8$

$\displaystyle 21$ and $\displaystyle 48$

Correct answer:

$\displaystyle 21$ and $\displaystyle 48$

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 $\displaystyle 7:16$

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

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

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Example Question #623 : Plane Geometry

Tri_sim_vt_series_cont_

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

Possible Answers:

145 $\displaystyle 145$ and 165 $\displaystyle 165$

$\displaystyle 9$ and $\displaystyle 13$

$\displaystyle 13$ and $\displaystyle 19$

200 $\displaystyle 200$ and 213 $\displaystyle 213$

Correct answer:

145 $\displaystyle 145$ and 165 $\displaystyle 165$

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 $\displaystyle 29:33$

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

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

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #621 : Plane Geometry

Example Question #622 : Plane Geometry

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

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

Example Question #623 : Plane Geometry

All Intermediate Geometry Resources

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