Congruent Triangles

What is the ASA congruence criterion?

• ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

• ASA congruence criterion states that if two sides of one triangle are congruent to two sides of another triangle, then the two triangles are congruent.

• ASA congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

• ASA congruence criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are congruent.

In triangle ABC, if angle A is 60 degrees, angle B is 40 degrees, and side AB is 5 cm, find the measure of angle C.

• 120

• 100

• 150

• 80

In triangle XYZ, if angle X is 90 degrees, angle Y is 30 degrees, and side XY is 8 cm, find the measure of angle Z.

• 90

• 45

• 60

• 120

True or False: 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.

• True

• Not enough information to determine

• Sometimes true

• False

True or False: 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.

• False

• Sometimes true

• Not enough information to determine

• True

In triangle PQR, if angle P is 50 degrees, angle Q is 70 degrees, and side PQ is 6 cm, find the measure of angle R.

• 60

• 80

• 40

• 90

In triangle DEF, if angle D is 45 degrees, angle E is 45 degrees, and side DE is 10 cm, find the measure of angle F.

• 90

• 30

• 120

• 60

What are the necessary conditions for two triangles to be congruent using the AAS congruence criterion?

• Side-Angle-Side

• Angle-Side-Angle

• Angle-Angle-Side

• Side-Side-Side

What are the necessary conditions for two triangles to be congruent using the ASA congruence criterion?

• Two pairs of corresponding congruent angles and a pair of corresponding congruent sides included between the two congruent angles.

• Two pairs of corresponding congruent angles and a pair of corresponding congruent sides not included between the two congruent angles.

• Two pairs of corresponding congruent sides and a pair of corresponding congruent angles.

• Two pairs of corresponding congruent angles and a pair of corresponding congruent sides not included between the two congruent angles.