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Common Core: High School - Geometry : Similarity, Right Triangles, & Trigonometry

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : Similarity Transformations Given Two Figures: Ccss.Math.Content.Hsg Srt.A.2

Which of the other triangles is similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$?

Plot10

Possible Answers:

Plot10.3

None of the answers.

Plot10.2

Plot10.1

Correct answer:

Plot10.1

Explanation:

Plot10.1

This is the correct answer because it has similar angles, and if we do some simple math, we can figure out what the missing angle is in the original picture.

Adding the two know angles and recalling that all interior angles of a triangle have a sum of 180 degrees, the following equation is constructed.

$180 = \measuredangle B + 10.0$ $\displaystyle 180 = \measuredangle B + 10.0$

Now solve for B, to figure out what the missing angle is.

$\measuredangle B = 170.0$ $\displaystyle \measuredangle B = 170.0$

Now if we look at the missing angle in the picture, it has the same angles.

The other pictures don't have similar answers.

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Example Question #8 : Similarity Transformations Given Two Figures: Ccss.Math.Content.Hsg Srt.A.2

Which of the other triangles is similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$?

Plot11

Possible Answers:

Plot11.2

Plot11.1

Plot11.3

None of the answers.

Correct answer:

Plot11.1

Explanation:

Plot11.1

This is the correct answer because it has similar angles, and if we do some simple math, we can figure out what the missing angle is in the original picture.

Adding the two know angles and recalling that all interior angles of a triangle have a sum of 180 degrees, the following equation is constructed.

$180 = \measuredangle B + 17.0$ $\displaystyle 180 = \measuredangle B + 17.0$

Now solve for B, to figure out what the missing angle is.

$\measuredangle B = 163.0$ $\displaystyle \measuredangle B = 163.0$

Now if we look at the missing angle in the picture, it has the same angles.

The other pictures don't have similar answers.

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Example Question #11 : Similarity Transformations Given Two Figures: Ccss.Math.Content.Hsg Srt.A.2

Which of the other triangles is similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$?

Plot12

Possible Answers:

Plot12.2

None of the answers.

Plot12.1

Plot12.3

Correct answer:

Plot12.1

Explanation:

Plot12.1

This is the correct answer because it has similar angles, and if we do some simple math, we can figure out what the missing angle is in the original picture.

Adding the two know angles and recalling that all interior angles of a triangle have a sum of 180 degrees, the following equation is constructed.

$180 = \measuredangle B + 27.0$ $\displaystyle 180 = \measuredangle B + 27.0$

Now solve for B, to figure out what the missing angle is.

$\measuredangle B = 153.0$ $\displaystyle \measuredangle B = 153.0$

Now if we look at the missing angle in the picture, it has the same angles.

The other pictures don't have similar answers.

Report an Error

Example Question #21 : Similarity, Right Triangles, & Trigonometry

Which of the other triangles is similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$?

Plot8

Possible Answers:

Plot7.1

Plot8.2

Plot8.1

None of the answers.

Correct answer:

Plot8.1

Explanation:

Plot8.1

This is the correct answer because it has similar angles, and if we do some simple math, we can figure out what the missing angle is in the original picture.

Adding the two known angles and recalling that all interior angles have a sum of 180 degrees.

$180 = \measuredangle B + 92.0$ $\displaystyle 180 = \measuredangle B + 92.0$

Now solve for B, to figure out what the missing angle is.

$\measuredangle B = 88.0$ $\displaystyle \measuredangle B = 88.0$

Now if we look at the missing angle in the picture, it has the same angles.

The other pictures don't have similar answers.

Report an Error

Example Question #1 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Given the black, green, and purple triangles below, determine which of the triangles are similar?
Hsg.srt.a.3 1

Possible Answers:

All triangles are similar.

The black and green triangle are similar.

The purple and black triangle are similar.

The green and purple triangle are similar.

None of the triangles are similar.

Correct answer:

The black and green triangle are similar.

Explanation:

To determine whether triangles are similar recall what "similar" means and the AA identity. To be "similar" triangles need to have congruent angles. Also recall that all triangles have interior angles that sum to 180 degrees.

Knowing this, look at the black triangle.

Screen shot 2016 07 15 at 2.33.19 pm

Two angles are given and the third can be calculated.

$180^\circ-66^\circ-58^\circ=56^\circ$ $\displaystyle 180^\circ-66^\circ-58^\circ=56^\circ$

Now, look at the green triangle.

Screen shot 2016 07 15 at 2.33.24 pm

$180^\circ-66^\circ-58^\circ=56^\circ$ $\displaystyle 180^\circ-66^\circ-58^\circ=56^\circ$

Now, look at the purple triangle.

Screen shot 2016 07 15 at 2.33.36 pm

$180^\circ-66^\circ-62^\circ=52^\circ$ $\displaystyle 180^\circ-66^\circ-62^\circ=52^\circ$

Since the black and green triangle have the same angle measurements, they are considered to be similar. The purple triangle only has one angle that is congruent to the other triangles thus, the purple triangle is not similar to either of the other two triangles.

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Example Question #2 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Given the black, green, and purple triangles below, determine which of the triangles are similar?

Hsg.srt.a.3 2

Possible Answers:

None of the triangles are similar.

All triangles are similar

The green and purple triangles are similar.

The black and green triangle are similar.

The black and purple triangles are similar.

Correct answer:

All triangles are similar

Explanation:

To determine whether triangles are similar recall what "similar" means and the AA criterion. To be "similar" triangles need to have congruent angles. Also recall that all triangles have interior angles that sum to 180 degrees.

Knowing this, look at the black triangle.

Screen shot 2016 07 15 at 2.33.19 pm

Two angles are given and the third can be calculated.

$180^\circ-66^\circ-58^\circ=56^\circ$ $\displaystyle 180^\circ-66^\circ-58^\circ=56^\circ$

Now, look at the green triangle.

Screen shot 2016 07 15 at 2.33.24 pm

$180^\circ-66^\circ-58^\circ=56^\circ$ $\displaystyle 180^\circ-66^\circ-58^\circ=56^\circ$

Now, look at the purple triangle.

Screen shot 2016 07 18 at 7.19.56 am

$180^\circ-66^\circ-56^\circ=58^\circ$ $\displaystyle 180^\circ-66^\circ-56^\circ=58^\circ$

Since the black and green triangle have the same angle measurements, they are considered to be similar. The purple triangle also has the same angle measurements as the black and green triangles thus, all three triangles are similar.

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Example Question #3 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Hsg.srt.a.3 3

The $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ above has $\measuredangle A=26^\circ$ $\displaystyle \measuredangle A=26^\circ$. Which of the following triangle measurements would be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$.

Possible Answers:

$\\\measuredangle G=23^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=23^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=26^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=26^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=36^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=36^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=24^\circ\\\measuredangle H=38^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=24^\circ\\\measuredangle H=38^\circ\\ \measuredangle I=118^\circ$

Correct answer:

$\\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$

Explanation:

To determine whether triangles are similar recall what "similar" means by the AA criterion. To be "similar" triangles need to have congruent angles. Also recall that all triangles have interior angles that sum to 180 degrees.

$\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ is given below. By the figure it is known that $\measuredangle B=118^\circ$ $\displaystyle \measuredangle B=118^\circ$ and by the statement, $\measuredangle A=26^\circ$ $\displaystyle \measuredangle A=26^\circ$. Knowing this information, the measure of the last angle can be calculated.

Hsg.srt.a.3 3

$180^\circ-118^\circ-26^\circ=36^\circ$ $\displaystyle 180^\circ-118^\circ-26^\circ=36^\circ$

Therefore, for a triangle to be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ by the AA criterion, the triangle must have angle measurements of 26, 36, and 118 degrees. Thus, $\bigtriangleup GHI$ $\displaystyle \bigtriangleup GHI$ is a similar triangle.

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Example Question #4 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Hsg.srt.a.3 3

The $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ above has $\measuredangle A=36^\circ$ $\displaystyle \measuredangle A=36^\circ$. Which of the following triangle measurements would be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$.

Possible Answers:

$\\\measuredangle G=23^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=23^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=36^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=36^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=26^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=26^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=24^\circ\\\measuredangle H=38^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=24^\circ\\\measuredangle H=38^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$

Correct answer:

$\\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=26^\circ\\\measuredangle H=36^\circ\\ \measuredangle I=118^\circ$

Explanation:

$\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ is given below. By the figure it is known that $\measuredangle B=118^\circ$ $\displaystyle \measuredangle B=118^\circ$ and by the statement, $\measuredangle A=36^\circ$ $\displaystyle \measuredangle A=36^\circ$. Knowing this information, the measure of the last angle can be calculated.

Hsg.srt.a.3 3

$180^\circ-118^\circ-36^\circ=26^\circ$ $\displaystyle 180^\circ-118^\circ-36^\circ=26^\circ$

Report an Error

Example Question #3 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Hsg.srt.a.3 5

The $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ above has $\measuredangle C=13^\circ$ $\displaystyle \measuredangle C=13^\circ$. Which of the following triangle measurements would be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$.

Possible Answers:

$\\\measuredangle G=13^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=13^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=24^\circ\\\measuredangle H=17^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=24^\circ\\\measuredangle H=17^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=17^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=131^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=131^\circ$

$\\\measuredangle G=17^\circ\\\measuredangle H=13^\circ\\ \measuredangle I=150^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=13^\circ\\ \measuredangle I=150^\circ$

$\\\measuredangle G=17^\circ\\\measuredangle H=15^\circ\\ \measuredangle I=148^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=15^\circ\\ \measuredangle I=148^\circ$

Correct answer:

$\\\measuredangle G=17^\circ\\\measuredangle H=13^\circ\\ \measuredangle I=150^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=13^\circ\\ \measuredangle I=150^\circ$

Explanation:

$\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ is given below. By the figure it is known that $\measuredangle A=17^\circ$ $\displaystyle \measuredangle A=17^\circ$ and by the statement, $\measuredangle C=13^\circ$ $\displaystyle \measuredangle C=13^\circ$. Knowing this information, the measure of the last angle can be calculated.

Hsg.srt.a.3 5

$180^\circ-17^\circ-13^\circ=150^\circ$ $\displaystyle 180^\circ-17^\circ-13^\circ=150^\circ$

Therefore, for a triangle to be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ by the AA criterion, the triangle must have angle measurements of 17, 13, and 150 degrees. Thus, $\bigtriangleup GHI$ $\displaystyle \bigtriangleup GHI$ is a similar triangle.

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Example Question #6 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Hsg.srt.a.3 5

The $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ above has $\measuredangle B=139^\circ$ $\displaystyle \measuredangle B=139^\circ$. Which of the following triangle measurements would be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$.

Possible Answers:

$\\\measuredangle G=24^\circ\\\measuredangle H=17^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=24^\circ\\\measuredangle H=17^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=13^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$ $\displaystyle \\\measuredangle G=13^\circ\\\measuredangle H=39^\circ\\ \measuredangle I=118^\circ$

$\\\measuredangle G=17^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=139^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=32^\circ\\ \measuredangle I=139^\circ$

$\\\measuredangle G=17^\circ\\\measuredangle H=24^\circ\\ \measuredangle I=139^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=24^\circ\\ \measuredangle I=139^\circ$

$\\\measuredangle G=17^\circ\\\measuredangle H=15^\circ\\ \measuredangle I=148^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=15^\circ\\ \measuredangle I=148^\circ$

Correct answer:

$\\\measuredangle G=17^\circ\\\measuredangle H=24^\circ\\ \measuredangle I=139^\circ$ $\displaystyle \\\measuredangle G=17^\circ\\\measuredangle H=24^\circ\\ \measuredangle I=139^\circ$

Explanation:

$\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ is given below. By the figure it is known that $\measuredangle A=17^\circ$ $\displaystyle \measuredangle A=17^\circ$ and by the statement, $\measuredangle B=139^\circ$ $\displaystyle \measuredangle B=139^\circ$. Knowing this information, the measure of the last angle can be calculated.

Hsg.srt.a.3 5

$180^\circ-17^\circ-139^\circ=24^\circ$ $\displaystyle 180^\circ-17^\circ-139^\circ=24^\circ$

Therefore, for a triangle to be similar to $\bigtriangleup ABC$ $\displaystyle \bigtriangleup ABC$ by the AA criterion, the triangle must have angle measurements of 17, 24, and 139 degrees. Thus, $\bigtriangleup GHI$ $\displaystyle \bigtriangleup GHI$ is a similar triangle.

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Similarity, Right Triangles, & Trigonometry

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #7 : Similarity Transformations Given Two Figures: Ccss.Math.Content.Hsg Srt.A.2

Example Question #8 : Similarity Transformations Given Two Figures: Ccss.Math.Content.Hsg Srt.A.2

Example Question #11 : Similarity Transformations Given Two Figures: Ccss.Math.Content.Hsg Srt.A.2

Example Question #21 : Similarity, Right Triangles, & Trigonometry

Example Question #1 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Example Question #2 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Example Question #3 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Example Question #4 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Example Question #3 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

Example Question #6 : Aa Criterion Using Similarity Transformations: Ccss.Math.Content.Hsg Srt.A.3

All Common Core: High School - Geometry Resources

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