Dec 12 Geometry Core 3 Congruency Theorems

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 their corresponding sides and angles are equal.

Front

What is the SSS Congruence Theorem?

Back

The SSS (Side-Side-Side) Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the ASA Congruence Theorem?

Back

The ASA (Angle-Side-Angle) Congruence Theorem 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 triangles are congruent.

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence 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 HL Congruence Theorem?

Back

The HL (Hypotenuse-Leg) Congruence 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 triangles are congruent.

Front

What additional information is needed to prove triangles congruent by SAS?

Back

To prove triangles congruent by SAS (Side-Angle-Side), you need to know that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which allows us to make conclusions about the triangles' properties.

Front

How can you determine if two triangles are congruent using the SSS theorem?

Back

Measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent by SSS.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent. Congruent triangles have equal corresponding sides and angles, while similar triangles have proportional sides and equal corresponding angles.

Front

What does the term 'included angle' refer to in triangle congruence?

Back

The included angle is the angle formed between two sides of a triangle. It is crucial in the ASA and SAS congruence theorems.