Angle-Angle Similarity

Front

What is Angle-Angle (AA) Similarity?

Back

Angle-Angle (AA) Similarity is a criterion for determining if two triangles are similar. If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If triangle A has angles of 30° and 60°, what are the angles of a similar triangle?

Back

A similar triangle will also have angles of 30° and 60°.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

How can you determine if two triangles are similar using AA similarity?

Back

To determine if two triangles are similar using AA similarity, check if two pairs of corresponding angles are equal.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle A has angles of 45°, 45°, and 90°, what are the angles of triangle B if it is similar to triangle A?

Back

Triangle B will also have angles of 45°, 45°, and 90°.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the sides of similar triangles?

Back

The sides of similar triangles are proportional to each other.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If triangle A has sides of lengths 3, 4, and 5, and triangle B is similar to triangle A with a scale factor of 2, what are the lengths of the sides of triangle B?

Back

The lengths of the sides of triangle B will be 6, 8, and 10.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

Can two triangles be similar if only one pair of angles is equal?

Back

No, two triangles cannot be similar if only one pair of angles is equal; at least two pairs of angles must be equal.

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

The AA similarity postulate allows us to conclude that two triangles are similar based solely on the equality of two angles.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle A has angles of 70° and 40°, what is the measure of the third angle?

Back

The third angle will be 70° (since the sum of angles in a triangle is 180°).

Tags

CCSS.8.G.A.5