Triangle Congruence: SSS, SAS, ASA, and AAS Explained

The video tutorial from Howard Community College covers the concept of triangle congruence. It explains how to logically derive the rules for triangle congruence, focusing on four main types: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS). Each type is explained with examples, demonstrating how congruent sides and angles lead to congruent triangles. The tutorial encourages understanding the logic behind these rules rather than just memorizing them.

What is the main idea behind side-side-side (SSS) congruence?

• If two triangles have three pairs of congruent sides, they are congruent.

• If two triangles have three pairs of congruent angles, they are congruent.

• If two triangles have two pairs of congruent sides and one pair of congruent angles, they are congruent.

• If two triangles have one pair of congruent sides and two pairs of congruent angles, they are congruent.

In the context of triangle congruence, what does SAS stand for?

• Side-Side-Angle

• Side-Angle-Side-Angle

• Side-Angle-Side

• Side-Side-Side

For SAS congruence, where must the congruent angle be located?

• At the midpoint of one of the congruent sides

• Anywhere in the triangle

• At the end of one of the congruent sides

• Between the two congruent sides

What is the key requirement for two triangles to be congruent under ASA congruence?

• Two pairs of congruent angles and the included side between them are congruent.

• Two pairs of congruent sides and the included angle between them are congruent.

• Three pairs of congruent angles are congruent.

• Three pairs of congruent sides are congruent.

In ASA congruence, what is the 'included side'?

• The side between the two congruent angles

• The side adjacent to one of the congruent angles

• The side opposite one of the congruent angles

• Any side of the triangle

What does AAS stand for in triangle congruence?

• Angle-Side-Angle

• Angle-Angle-Side-Angle

• Angle-Angle-Side

• Angle-Side-Side

How can you prove that two triangles are congruent using AAS?

• By showing three pairs of congruent angles.

• By showing two pairs of congruent sides and the included angle between them.

• By showing three pairs of congruent sides.

• By showing two pairs of congruent angles and a pair of congruent sides not between them.

What is the sum of the interior angles of any triangle?

• 180 degrees

• 360 degrees

• 90 degrees

• 270 degrees

Which congruence rule can be derived from knowing two pairs of congruent angles and one pair of congruent sides?

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

• Angle-Side-Angle (ASA)

What are the four basic rules for triangle congruence discussed in the video?

• SSS, SAS, ASA, AAA

• SSS, SAS, SSA, ASA

• SSS, SAS, ASA, AAS

• SSS, SAS, SSA, AAS