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 equal 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 two triangles have one angle of equal measure, can they be similar?

Back

No, having only one angle equal is not sufficient to prove similarity. You need at least two angles to apply AA similarity.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of the corresponding sides of similar triangles are proportional.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If triangle A has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

A similar triangle will also have angles of 30°, 60°, and 90°.

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

Check if two angles of one triangle are equal to two angles of another triangle. If they are, the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What is the significance of the third angle in similar triangles?

Back

If two angles are known to be equal, the third angle must also be equal due to the triangle sum theorem (sum of angles in a triangle is 180°).

Tags

CCSS.HSG.SRT.A.2

Front

Can two triangles with sides in the ratio 2:3 be similar?

Back

Not necessarily. The angles must also be equal for the triangles to be similar.

Tags

CCSS.HSG.SRT.A.2

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180°.

Tags

CCSS.8.G.A.5

Front

If triangle A is similar to triangle B, and the length of a side in triangle A is 4 cm, what is the corresponding side in triangle B if the ratio of similarity is 1:2?

Back

The corresponding side in triangle B would be 8 cm.