Lesson 15A Congruent Triangles/Postulates

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.

Tags

CCSS.8.G.A.2

Front

What does the SSS postulate state?

Back

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

Tags

CCSS.HSG.SRT.B.5

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.

Tags

CCSS.HSG.SRT.B.5

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.

Tags

CCSS.HSG.SRT.B.5

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 a non-included side of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the SSA condition? Is it a valid congruence theorem?

Back

SSA (Side-Side-Angle) is not a valid congruence theorem because it does not guarantee triangle congruence.

Tags

CCSS.8.G.A.2

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.

Tags

CCSS.8.G.A.2

Front

What is the importance of the included angle in the SAS postulate?

Back

The included angle is crucial because it ensures that the two triangles are not just similar but congruent.

Tags

CCSS.HSG.SRT.B.5

Front

How can you prove triangles are congruent using the ASA postulate?

Back

By showing that two angles and the side between them in one triangle are equal to the corresponding two angles and side in another triangle.

Tags

CCSS.HSG.SRT.B.5

Front

What is a counterexample to the SSA condition?

Back

Two triangles can have two sides equal and a non-included angle equal, but they may not be congruent (e.g., the ambiguous case of triangles).

Tags

CCSS.8.G.A.2