Triangle Congruence Concepts and Theorems

This video tutorial explains how to determine if two triangles are congruent. It reviews the postulates used to prove congruence, such as side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS). The tutorial provides examples to illustrate these concepts and highlights cases where triangles cannot be proven congruent. Key points include the importance of corresponding parts and the correct order of vertices in congruence statements.

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

• They must have the same perimeter.

• They must have the same area.

• Their corresponding angles and sides must be congruent.

• They must be similar.

What is the CPCTC theorem used for?

• To prove triangles have the same perimeter.

• To prove triangles have the same area.

• To prove corresponding parts of congruent triangles are congruent.

• To prove triangles are similar.

Which of the following is NOT a valid postulate for proving triangle congruence?

• Side-Side-Side

• Angle-Side-Angle

• Side-Angle-Side

• Angle-Angle-Angle

In the first example, which postulate is used to prove the triangles are congruent?

• Angle-Angle-Side

• Side-Side-Side

• Angle-Side-Angle

• Side-Angle-Side

When listing vertices of congruent triangles, what must be ensured?

• They are listed randomly.

• They are listed in reverse order.

• They are listed in corresponding order.

• They are listed alphabetically.

In the second example, what is the reason for the triangles being congruent?

• They have two pairs of congruent angles.

• They have the same perimeter.

• They have three pairs of congruent sides.

• They have two pairs of congruent sides and one pair of congruent angles.

What is the significance of a midpoint in proving triangle congruence?

• It is irrelevant to congruence.

• It bisects an angle.

• It creates a right angle.

• It divides a segment into two congruent segments.

In the third example, why can't the triangles be proven congruent?

• They are not similar.

• They have no congruent sides.

• They have no congruent angles.

• The given information does not fit any congruence postulate.

Which of the following is a valid reason for triangles not being congruent?

• They have different colors.

• They have different shapes.

• The information does not satisfy any congruence postulate.

• They are not drawn to scale.

What is the role of vertical angles in triangle congruence?

• They are always congruent.

• They are never congruent.

• They are irrelevant to congruence.

• They are congruent only if the triangles are congruent.