Triangle Congruence Theorems Explained

Miss Mathis explains how to identify congruent triangles using five theorems: SSS, SAS, HL, ASA, and AAS. She introduces the concepts of included angles and sides, and reviews the reflexive property of congruence. The video includes practice problems to apply these theorems and concludes with a summary of the methods to prove triangle congruence.

What is an included angle in a triangle?

• An angle formed by two non-adjacent sides

• An angle formed by two adjacent sides

• An angle formed by two opposite sides

• An angle formed by the base and height

Which theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent?

• Side-Angle-Side (SAS)

• Hypotenuse-Leg (HL)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

In the Side-Angle-Side (SAS) theorem, what must be true about the angle?

• It must be an exterior angle

• It must be an obtuse angle

• It must be an included angle

• It must be a right angle

What additional information is needed to use the Hypotenuse-Leg (HL) theorem?

• The triangles must be scalene

• The triangles must be right triangles

• The triangles must be equilateral

• The triangles must be isosceles

Which theorem can be used if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle?

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

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

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

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

• If two angles and a non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then 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, then the triangles are congruent.

What does the reflexive property of congruence state?

• A side of a triangle is congruent to a side of another triangle

• A side of a triangle is congruent to itself

• An angle of a triangle is congruent to an angle of another triangle

• An angle of a triangle is congruent to itself

In the given problem, which side is congruent to itself by the reflexive property?

• WY

• LK

• UN

• LN

Which theorem is used to prove that triangles are congruent if they have three pairs of congruent sides?

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

• Angle-Angle-Side (AAS)

What is the correct congruence statement for triangles with sides ST, QR, and RT?

• Triangle STR is congruent to triangle QRS

• Triangle STR is congruent to triangle QTR

• Triangle STR is congruent to triangle QRT

• Triangle STR is congruent to triangle QTS