Dec 12 Geometry Core 2 Congruency Theorems

Front

What does congruency mean in geometry?

Back

Congruency in geometry means that two figures have the same shape and size. This can be established through various congruency theorems.

Front

What are the main congruency theorems for triangles?

Back

The main congruency theorems for triangles are: 1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. ASA (Angle-Side-Angle) 4. AAS (Angle-Angle-Side) 5. HL (Hypotenuse-Leg for right triangles).

Front

What is the SSS congruency theorem?

Back

The SSS (Side-Side-Side) congruency 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 SAS congruency theorem?

Back

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

Front

What is the ASA congruency theorem?

Back

The ASA (Angle-Side-Angle) congruency 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 congruency theorem?

Back

The AAS (Angle-Angle-Side) congruency 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 congruency theorem?

Back

The HL (Hypotenuse-Leg) congruency theorem applies to right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

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

Back

To determine if two triangles are congruent using the SSS theorem, measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

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

Back

To determine if two triangles are congruent using the SAS theorem, measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, the triangles are congruent.

Front

What additional information is needed to apply the ASA theorem?

Back

To apply the ASA theorem, you need to know two angles and the length of the side between them in one triangle, and the corresponding angles and side in the other triangle.