Triangle Congruence Review # 1

Front

What does it mean for two triangles to be congruent?

Back

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

Front

What is the SAS (Side-Angle-Side) Congruence Postulate?

Back

The SAS Postulate states that if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is also equal, then the two triangles are congruent.

Front

What is the ASA (Angle-Side-Angle) Congruence Postulate?

Back

The ASA Postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Theorem 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.

Front

What is the definition of CPCTC?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent', which means that if two triangles are proven to be congruent, then all their corresponding sides and angles are also congruent.

Front

What is the H-L (Hypotenuse-Leg) Theorem?

Back

The H-L Theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

If ∆MNO ≅ ∆PQR, what can we conclude about the corresponding sides and angles?

Back

We can conclude that MN = PQ, NO = QR, and ∠M ≅ ∠P, ∠N ≅ ∠Q, ∠O ≅ ∠R.

Front

How do you find the measure of an angle in congruent triangles?

Back

If two triangles are congruent, the measures of their corresponding angles are equal. You can set the expressions for the angles equal to each other and solve for the variable.

Front

What is the significance of drawing a picture when solving triangle congruence problems?

Back

Drawing a picture helps visualize the problem, making it easier to identify corresponding parts and apply congruence postulates or theorems.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size (corresponding angles are equal, and corresponding sides are proportional).