Triangle Similarity Theorems and Postulates

What is the primary condition for two triangles to be considered similar according to the Angle-Angle Similarity Theorem?

• They must have the same area.

• They must be right triangles.

• They must have two angles of the same measure.

• They must have identical side lengths.

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CCSS.HSG.SRT.A.2

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How many angles need to match in measure for two triangles to be similar by the Angle-Angle Similarity Theorem?

• Four

• One

• Two

• Three

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CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

If two angles in a triangle are 90 and 20 degrees, what is the measure of the third angle?

• 50 degrees

• 60 degrees

• 70 degrees

• 40 degrees

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CCSS.HSG.CO.C.10

Why does knowing two angles of a triangle allow you to determine the third angle?

• Because the sum of angles in a triangle is always 180 degrees.

• Because the sum of angles in a triangle is variable.

• Because the sum of angles in a triangle is always 200 degrees.

• Because the sum of angles in a triangle is always 90 degrees.

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CCSS.HSG.CO.C.10

What should you do if you want a more detailed explanation of the Angle-Angle Similarity Theorem?

• Watch the long form video linked in the description.

• Consult a mathematics textbook.

• Ignore the details and move on.

• Ask a mathematics teacher.

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CCSS.HSG.SRT.A.2

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CCSS.HSG.SRT.B.5

What similarity theorem would prove that these triangles are similar?

• SAS∼
• SSS∼
• AA∼
• Side Splitter

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CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.B.5

Mark the angle pairs which are congruent due to the presence of transversal HK which would help prove that triangles RXH and KXN are congruent.

• ∠RXK ≅ ∠HXN

• ∠RHX ≅ ∠NKX

• ∠CRN ≅ ∠TNC

• ∠RHX ≅ ∠KXN

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CCSS.HSG.CO.C.9

CCSS.HSG.SRT.B.5

Are the triangles similar?

• Yes, by AA
• Not similar
• Yes, by SAS
• Yes, by SSS

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CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.B.5

Are the triangles similar? If so, how?

• Similar by AA

• Similar by SAS

• Similar by SSS

• Not similar

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CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.B.5

What does the SSS similarity theorem state about two triangles?

• They are similar if they have the same color.

• They are similar if they are of the same size.

• They are similar if their sides' lengths are proportional.

• They are similar if their angles are equal.

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CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.B.5