Congruent Triangles (SSS & SAS)

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, meaning they have the same shape and size. It is often written in the form ΔABC ≅ ΔDEF.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side'. It is a criterion for triangle congruence that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for 'Side-Angle-Side'. It is a criterion for triangle congruence that states 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

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

Back

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

Front

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

Back

To determine if two triangles are congruent using SAS, measure two sides and the included angle of each triangle. If the two sides and the angle in one triangle are equal to the corresponding two sides and angle in the other triangle, the triangles are congruent.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being measured. It is crucial because it ensures that the triangles are congruent in shape, not just in size.

Front

Can two triangles be congruent if only two sides are equal?

Back

No, two triangles cannot be determined to be congruent with only two sides equal. You need either the third side or the included angle to apply SSS or SAS.

Front

What does it mean if two triangles are not congruent?

Back

If two triangles are not congruent, it means they do not have the same shape and size. This can be due to differences in side lengths or angles.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that two triangles are identical in shape and size, while similarity means that two triangles have the same shape but may differ in size.

Front

Provide an example of a congruence statement using SSS. What does it indicate?

Back

Example: ΔABC ≅ ΔDEF indicates that triangle ABC is congruent to triangle DEF, meaning all corresponding sides are equal in length.