Proving Triangle Congruence: SSS and SAS Methods

This video tutorial covers the methods of proving triangles congruent using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. It explains the concepts of included sides and angles, provides detailed examples of proofs using these postulates, and includes practice questions with solutions to reinforce understanding.

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

• 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 two triangles are congruent.

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

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

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

Which segment is included between angles A and B in triangle ABC?

• Segment AC

• Segment AB

• Segment XY

• Segment BC

What is an included angle in a triangle?

• An angle that is between two angles of a triangle.

• An angle that is formed by extending one side of the triangle.

• An angle that is outside the triangle.

• An angle that is between two sides of a triangle.

What does the Side-Angle-Side (SAS) postulate state?

• 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 two triangles are congruent.

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

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

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

In the diagram, which angles are congruent by the vertical angle theorem?

• Angles A and B

• Angles C and D

• Angles G and H

• Angles E and F

Which postulate can be used to prove that triangle FGE is congruent to triangle HGE?

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

If segment LM is parallel to segment NO, which angles are congruent by the AIA theorem?

• Angles 3 and 4

• Angles 5 and 6

• Angles 7 and 8

• Angles 1 and 2

What sides include angle Y in triangle XYZ?

• Sides XY and YZ

• Sides XZ and YZ

• Sides XZ and YX

• Sides XY and XZ

Which angle is included between segments XY and XZ?

• Angle Z

• Angle W

• Angle Y

• Angle X

Can the triangles ABC and DEF be proven congruent using the given information: angle B is congruent to angle E, segment BA is congruent to segment ED, and segment AC is congruent to segment DF?

• No, because the sides are not congruent

• No, because the angle is not included between the congruent sides

• Yes, by SAS postulate

• Yes, by SSS postulate