Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What does AA similarity criterion stand for?

Back

AA stands for Angle-Angle. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What does SSS similarity criterion stand for?

Back

SSS stands for Side-Side-Side. If the corresponding sides of two triangles are in proportion, the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does SAS similarity criterion stand for?

Back

SAS stands for Side-Angle-Side. If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

How can you determine if two triangles are not similar?

Back

If none of the similarity criteria (AA, SSS, SAS) are satisfied, the triangles are not similar.

Tags

CCSS.HSG.SRT.B.5

Front

If triangle ABC is similar to triangle DEF, what can be said about their angles?

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Tags

CCSS.HSG.SRT.A.2

Front

If the sides of triangle ABC are 3, 4, and 5, and the sides of triangle DEF are 6, 8, and 10, are the triangles similar?

Back

Yes, by SSS postulate, since the sides are in proportion (3:6, 4:8, 5:10).

Tags

CCSS.HSG.SRT.A.2

Front

If triangle ABC has angles of 30° and 60°, what is the measure of the third angle?

Back

The third angle is 90°, since the sum of angles in a triangle is 180°.

Tags

CCSS.8.G.A.5

Front

If two triangles have one angle of 60° and the other angles are unknown, can we determine similarity?

Back

No, we need at least two angles to apply the AA criterion for similarity.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Tags

CCSS.HSG.SRT.A.2