Proving Triangle Congruence: SSS and SAS Methods

Mrs. Angel introduces congruent triangles and explains two shortcuts for proving their congruence: Side-Side-Side (SSS) and Side-Angle-Side (SAS). The video covers the properties of congruent triangles, including corresponding sides and angles, and demonstrates how to use SSS and SAS theorems to prove congruence. Examples are provided to illustrate these concepts, and students are encouraged to practice identifying congruent triangles using these methods.

What do we know about the corresponding sides of congruent triangles?

• They are not necessarily equal.

• They are always equal.

• They are sometimes equal.

• They are never equal.

Which of the following is true about the corresponding angles of congruent triangles?

• They are sometimes congruent.

• They are never congruent.

• They are not related.

• They are always congruent.

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

• If one side of one triangle is congruent to one side of another triangle, the triangles are congruent.

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

• If all angles of one triangle are congruent to all angles of another triangle, the triangles are congruent.

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

In the SSS theorem, what information is needed to conclude that two triangles are congruent?

• Two pairs of congruent sides.

• Three pairs of congruent angles.

• Two pairs of congruent sides and one pair of congruent angles.

• Three pairs of congruent sides.

If side JL is congruent to side MN, and K is the midpoint of both JN and LM, what can we conclude?

• Triangles JLK and NMK are congruent by SSS.

• Triangles JLK and NMK are congruent by SAS.

• Triangles JLK and NMK are congruent by ASA.

• Triangles JLK and NMK are not congruent.

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

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

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

• If all angles of one triangle are congruent to all angles of another triangle, the triangles are congruent.

In the SAS theorem, what is meant by the 'included angle'?

• Any angle in the triangle.

• The angle adjacent to the congruent sides.

• The angle between the two congruent sides.

• The angle opposite the congruent sides.

If side AB is congruent to side CB, and BD bisects angle ABC, what can we conclude?

• Triangles ABD and CBD are not congruent.

• Triangles ABD and CBD are congruent by ASA.

• Triangles ABD and CBD are congruent by SAS.

• Triangles ABD and CBD are congruent by SSS.

What is the significance of a shared side in proving triangle congruence?

• It can be used as one of the congruent sides in the SSS or SAS theorem.

• It cannot be used to prove congruence.

• It is irrelevant to triangle congruence.

• It only matters in the ASA theorem.

If BC is congruent to DC, AC is congruent to EC, and angle ACB is congruent to angle ECD, what can we conclude?

• Triangles ACB and ECD are congruent by SAS.

• Triangles ABC and DEF are congruent by SAS.

• Triangles ABC and DEF are congruent by SSS.

• Triangles ACB and ECD are not congruent.