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Flashcards: 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

The black and green triangle are similar.

None of the triangles are similar.

All triangles are similar.

The purple and black triangle are similar.

The green and purple triangle are similar.

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Flashcards: 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

Your answer:

None of the triangles are similar.

Your answer:

All triangles are similar.

Your answer:

The purple and black triangle are similar.

Your answer:

The green and purple triangle 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.

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

Now, look at the green triangle.

Screen shot 2016 07 15 at 2.33.24 pm

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

Now, look at the purple triangle.

Screen shot 2016 07 15 at 2.33.36 pm

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

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.

Flashcards: 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

The green and purple triangles are similar.

All triangles are similar

The black and purple triangles are similar.

None of the triangles are similar.

The black and green triangle are similar.

Report an Error Copyright Notice

Flashcards: 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

Your answer:

The green and purple triangles are similar.

Your answer:

The black and purple triangles are similar.

Your answer:

None of the triangles are similar.

Your answer:

The black and green triangle 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.

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

Now, look at the green triangle.

Screen shot 2016 07 15 at 2.33.24 pm

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

Now, look at the purple triangle.

Screen shot 2016 07 18 at 7.19.56 am

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

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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All Common Core: High School - Geometry Resources

Flashcards: AA Criterion using Similarity Transformations: CCSS.Math.Content.HSG-SRT.A.3

Flashcards: AA Criterion using Similarity Transformations: CCSS.Math.Content.HSG-SRT.A.3

Flashcards: AA Criterion using Similarity Transformations: CCSS.Math.Content.HSG-SRT.A.3

Flashcards: AA Criterion using Similarity Transformations: CCSS.Math.Content.HSG-SRT.A.3

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