Proving Triangle Congruence with ASA and AAS

The video tutorial covers lesson 45 on proving triangles congruent using the ASA and AAS postulates. It begins with an introduction to the concepts of ASA and AAS, explaining how two triangles can be proven congruent if certain conditions are met. The ASA postulate is detailed with examples, showing how two angles and the included side can establish congruence. The video then transitions to the AAS theorem, explaining how two angles and a non-included side can also prove congruence. Each section includes practical examples and proofs to illustrate the concepts, helping students understand the application of these geometric principles.

What does the ASA postulate state?

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

• If two angles and the included side of one triangle are congruent to three angles 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.

• 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.

In the example with triangles ABC and DEF, which sides are the included sides?

• AB and CD

• AC and DF

• BC and EF

• AB and DE

What is the first step in proving triangle ABE is congruent to triangle CDE?

• Identifying the parallel lines

• Marking the given information

• Drawing the triangles

• Listing the given information

Which angles are alternate interior angles when AB is parallel to CD and AC is the transversal?

• Angles A and C

• Angles B and D

• Angles A and B

• Angles C and D

What is the final step in proving triangle ABE is congruent to triangle CDE using the ASA postulate?

• Marking the congruent sides

• Listing the given information

• Stating the congruence by ASA

• Identifying the transversal

What does the AAS postulate state?

• 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.

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

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

In the AAS postulate example, which side is the non-included side?

• AC

• AB

• DE

• BC

What is the first step in proving segment AB is congruent to segment CD?

• Identifying the parallel lines

• Marking the given information

• Listing the given information

• Drawing the triangles

Which angles are alternate interior angles when AD is parallel to BC and BD is the transversal?

• Angles B and D

• Angles A and C

• Angles C and D

• Angles CBD and ADB

What is the final step in proving segment AB is congruent to segment CD using the AAS postulate?

• Stating the congruence by AAS

• Marking the congruent sides

• Listing the given information

• Identifying the transversal