Determining Similarity in Triangles Using AA Criterion

The video tutorial explains how to determine if two triangles are similar using the angle-angle (AA) similarity postulate. It begins with an introduction to the concept of similar triangles and the third angle theorem, which states that if two angles in one triangle are congruent to two angles in another triangle, the third angles must also be congruent. The tutorial then covers the AA similarity postulate, which simplifies the process by confirming similarity if two angles are congruent. Several examples are provided to illustrate the application of these concepts, including cases with non-similar triangles and the use of parallel lines to establish similarity.

What theorem states that if two angles of one triangle are congruent to two angles of another, the third angles are also congruent?

• Third Angle Theorem

• Side-Angle-Side Postulate

• Pythagorean Theorem

• Angle-Side-Angle Postulate

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CCSS.HSG.CO.B.7

If two angles in different triangles measure 79 degrees and 47 degrees, what is the measure of the third angle?

• 64 degrees

• 54 degrees

• 84 degrees

• 74 degrees

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CCSS.8.G.A.5

According to the angle-angle similarity postulate, what is required for two triangles to be considered similar?

• All sides of both triangles must be proportional

• All angles of both triangles must be congruent

• Two sides of one triangle are proportional to two sides of another triangle

• Two angles of one triangle are congruent to two angles of another triangle

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CCSS.HSG.SRT.A.2

What does the angle-angle similarity postulate save us from having to do?

• Prove that the triangles are congruent

• Calculate the area of the triangles

• Measure all sides of the triangles

• Determine the measure of the third angle

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CCSS.HSG.SRT.B.5

What property do corresponding angles of similar triangles exhibit?

• They are proportional

• They are congruent

• They are supplementary

• They are complementary

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CCSS.HSG.SRT.A.2

In the example where triangles were not similar, what was the measure of the third angle calculated for the large triangle?

• 36 degrees

• 34 degrees

• 33 degrees

• 35 degrees

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CCSS.HSG.SRT.A.2

If the sum of two angles in a triangle is 100 degrees, what is the measure of the third angle?

• 85 degrees

• 80 degrees

• 90 degrees

• 70 degrees

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CCSS.8.G.A.5

How should the vertices of similar triangles be listed?

• In numerical order

• In alphabetical order

• In corresponding order

• In random order

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CCSS.HSG.SRT.A.2

What is the correct way to denote that triangle ABC is similar to another triangle with vertices labeled as DEF, given angle correspondences?

• Triangle ABC is similar to triangle DFE

• Triangle ABC is similar to triangle EFD

• Triangle ABC is similar to triangle DEF

• Triangle ABC is similar to triangle FED

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CCSS.8.G.A.2

CCSS.HSG.CO.B.6

What geometric condition was used to establish similarity in the final example?

• Equal perimeter

• Congruent diagonals

• Equal side lengths

• Parallel lines cut by a transversal

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CCSS.HSG.SRT.A.2