Proving Triangle Congruence: SSS, SAS, ASA, AAS

What does the Side-Side-Side (SSS) postulate state?

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

• If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

• If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

In the example with triangles GHJ and KJL, what theorem is used to prove that GL is congruent to KL?

• Alternate Interior Angles Theorem

• Angle Bisector Theorem

• Midpoint Theorem

• Reflexive Property

What does the Side-Angle-Side (SAS) postulate require to prove triangle congruence?

• Two angles and a non-included side

• Two sides and the included angle

• Three sides

• Two angles and the included side

In the example with triangles WXZ and YXZ, which property is used to state that XZ is congruent to itself?

• Midpoint Theorem

• Reflexive Property

• Angle Bisector Theorem

• Alternate Interior Angles Theorem

What does the Angle-Side-Angle (ASA) postulate require to prove triangle congruence?

• Two angles and a non-included side

• Two sides and the included angle

• Three sides

• Two angles and the included side

In the example with triangles PQS and RQS, what is the reason given for angle PQS being congruent to angle RQS?

• Alternate Interior Angles Theorem

• Reflexive Property

• Angle Bisector Theorem

• Midpoint Theorem

What does the Angle-Angle-Side (AAS) postulate require to prove triangle congruence?

• Three sides

• Two sides and the included angle

• Two angles and a non-included side

• Two angles and the included side

In the example with triangles ACD and ECB, which property is used to state that angle C is congruent to itself?

• Reflexive Property

• Midpoint Theorem

• Alternate Interior Angles Theorem

• Angle Bisector Theorem

Which theorem is used to state that angle RQU is congruent to angle STU in the example with triangles RQU and STU?

• Angle Bisector Theorem

• Vertical Angles Theorem

• Midpoint Theorem

• Alternate Interior Angles Theorem

In the summary, which angles are mentioned as being congruent due to the Alternate Interior Angles Theorem?

• Angles formed by a transversal intersecting parallel lines

• Angles formed by vertical lines

• Angles formed by a bisector

• Angles formed by a midpoint