Congruent and Similar Triangles

Front

What does it mean for two triangles to be similar?

Back

Two 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

What is the AA criterion for triangle similarity?

Back

The AA (Angle-Angle) criterion states that 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 is the SSS criterion for triangle similarity?

Back

The SSS (Side-Side-Side) criterion states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What is the SAS criterion for triangle similarity?

Back

The SAS (Side-Angle-Side) criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have exactly the same size and shape, meaning all corresponding sides and angles are equal.

Tags

CCSS.8.G.A.2

Front

What is the AAS criterion for triangle congruence?

Back

The AAS (Angle-Angle-Side) criterion states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the ASA criterion for triangle congruence?

Back

The ASA (Angle-Side-Angle) criterion states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the SAS criterion for triangle congruence?

Back

The SAS (Side-Angle-Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the corresponding included angle of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

Can two triangles be congruent if they have two sides and a non-included angle equal?

Back

No, this is known as the SSA (Side-Side-Angle) condition, which does not guarantee congruence.

Tags

CCSS.8.G.A.2

Front

What is the relationship between similar triangles and their areas?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.