Triangle Congruency

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SAS postulate state?

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

What does the ASA postulate state?

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 does the AAS postulate state?

Back

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 SSA condition in triangle congruency?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruency; it can lead to ambiguous cases.

Front

How do you denote congruence between two triangles?

Back

Using the symbol '≅', for example, ΔABC ≅ ΔDEF.

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal.

Front

If m∠R = 34° and m∠L = 81°, how do you find m∠J in triangle RJL?

Back

Use the triangle sum theorem: m∠J = 180° - (m∠R + m∠L) = 180° - (34° + 81°) = 65°.

Front

What is the triangle sum theorem?

Back

The sum of the interior angles of a triangle is always 180°.

Front

What is the definition of corresponding angles?

Back

Angles that are in the same relative position at each intersection where a straight line crosses two others.