Similarity Applications and Proportionality

If two angles of one triangle are congruent to two angles of another triangle, then what can be said about the two triangles?

• The two triangles are parallel.

• The two triangles are similar.

• The two triangles are congruent.

• The two triangles are perpendicular.

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CCSS.HSG.CO.B.7

In the AA similarity theorem, what does AA stand for?

• Area-Area

• Apple-Apple

• Angle-Angle

• Arrow-Arrow

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CCSS.HSG.SRT.A.2

What is the significance of the AA similarity theorem in geometry?

• The AA similarity theorem is used to calculate the area of a triangle

• The AA similarity theorem is only applicable to right-angled triangles

• The AA similarity theorem is used to find the sum of the angles in a triangle

• The significance of the AA similarity theorem is that it provides a quick and easy way to determine if two triangles are similar without having to measure all their sides.

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CCSS.HSG.SRT.A.2

Can you provide an example of how the AA similarity theorem is used to solve a problem?

• Using the Pythagorean theorem to find the measures of the corresponding sides

• Applying the Law of Sines to determine the unknown angles

• Using the AA similarity theorem to find the area of the triangles

• Identifying congruent angles in two triangles and using the proportionality of corresponding sides to solve for unknown measures.

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CCSS.HSG.SRT.B.5

What are the conditions for the AA similarity theorem to be applicable?

• The triangles have equal side lengths

• The triangles have a common vertex

• The triangles are both equilateral

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

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CCSS.HSG.SRT.A.2

Explain the concept of corresponding angles in the context of the AA similarity theorem.

• Corresponding angles of similar triangles are equal.

• Corresponding angles of similar triangles are not equal.

• Corresponding angles of similar triangles are always obtuse.

• Corresponding angles of similar triangles are always acute.

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CCSS.HSG.SRT.A.2

What are the practical applications of the AA similarity theorem?

• Calculating the area of a circle

• Solving equations in algebra

• The practical applications of the AA similarity theorem include solving problems in geometry, such as determining the similarity of two triangles and finding unknown side lengths or angles.

• Determining the boiling point of a substance

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CCSS.HSG.SRT.A.2

How can the AA similarity theorem be used to prove two triangles similar?

• By proving that the two triangles have the same area

• We can use the AA similarity theorem to prove two triangles similar by showing that two angles of one triangle are congruent to two angles of the other triangle.

• By demonstrating that the two triangles have the same perimeter

• By showing that two sides of one triangle are congruent to two sides of the other triangle

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CCSS.HSG.SRT.B.5

Two objects that are the same shape but not the same size are _______.

• Congruent

• Vertical

• Similar

• Complementary 

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CCSS.8.G.A.2

CCSS.HSG.CO.B.6

The pair of figures is similar. Find the missing side.

• x = 1

• x = 3

• x = 9

• x = 5

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CCSS.HSG.SRT.A.2