Triangle Congruence Theorems

Front

What does SAS stand for in triangle congruence theorems?

Back

SAS stands for Side-Angle-Side, which is a theorem that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What does ASA stand for in triangle congruence theorems?

Back

ASA stands for Angle-Side-Angle, which is a theorem that states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What does AAS stand for in triangle congruence theorems?

Back

AAS stands for Angle-Angle-Side, which is a theorem that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What does the SSS theorem state?

Back

The SSS theorem stands for Side-Side-Side, which states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the AAA condition in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which states that if three angles of one triangle are congruent to three angles of another triangle, the triangles are similar but not necessarily congruent.

Tags

CCSS.HSG.SRT.B.5

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning \overline{AB} \cong \overline{AB}.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (vertical) angles are congruent.

Tags

CCSS.HSG.CO.C.9

Front

What is the purpose of triangle congruence theorems?

Back

Triangle congruence theorems are used to prove that two triangles are congruent, meaning they have the same size and shape.

Tags

CCSS.HSG.SRT.B.5

Front

How can you prove triangles are congruent using the SAS theorem?

Back

To prove triangles are congruent using the SAS theorem, you need to show that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Tags

CCSS.HSG.SRT.B.5

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to infer properties about the triangles, such as side lengths and angle measures, which can be used in various geometric proofs and applications.

Tags

CCSS.8.G.A.2