Congruent Triangles

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

If \( \Delta UVW \cong \Delta DEF \), what can we say about the corresponding sides?

Back

The corresponding sides are equal: \( \overline{UW} \cong \overline{DF} \), \( \overline{VW} \cong \overline{EF} \), and \( \overline{UV} \cong \overline{DE} \).

Front

What is the symbol for congruence in geometry?

Back

The symbol for congruence is \( \cong \).

Front

If \( \Delta JKL \cong \Delta RST \), what can we conclude about the angles?

Back

The corresponding angles are equal: \( \angle J \cong \angle R \), \( \angle K \cong \angle S \), and \( \angle L \cong \angle T \).

Front

What is the Side-Side-Side (SSS) Congruence Postulate?

Back

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

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

Back

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 Side-Angle-Side (SAS) Congruence Postulate?

Back

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

If \( \Delta WXY \cong \Delta HJI \), what is the relationship between their angles?

Back

The corresponding angles are equal: \( \angle W \cong \angle H \), \( \angle X \cong \angle J \), and \( \angle Y \cong \angle I \).

Front

What is the Hypotenuse-Leg (HL) Congruence Theorem?

Back

In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent.

Front

If \( \Delta ABC \cong \Delta DEF \), how can we write another congruence statement?

Back

We can write \( \Delta CBA \cong \Delta FED \) or any other permutation of the vertices that maintains the correspondence.