Proving Triangle Congruence with SSS, SAS & HL Theorems

The video tutorial covers the concept of congruent triangles using theorems such as SSS, SAS, and HL. It explains the importance of included angles and the reflexive property in proving congruence. The tutorial includes step-by-step problem-solving to demonstrate how to determine if triangles are congruent, emphasizing the need for logical reasoning and proof. The video also touches on angle relationships in parallel lines and their role in congruence proofs.

What are the three theorems used to prove triangle congruence?

• AAA, AAS, ASA

• ASA, AAS, SSA

• SSS, SAS, HL

• SSA, SSS, SAS

Tags

CCSS.HSG.SRT.B.5

What does the SSS theorem state?

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

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

Tags

CCSS.HSG.SRT.B.5

What is an included angle?

• An angle that is outside the triangle.

• An angle that is between two non-congruent sides.

• An angle that is between two congruent sides.

• An angle that is not part of the triangle.

What does the SAS theorem state?

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

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

• If two sides and a non-included angle of one triangle are congruent to two sides and a non-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.

Tags

CCSS.HSG.SRT.B.5

What is the hypotenuse in a right triangle?

• The side that forms the right angle.

• The side opposite the smallest angle.

• The side opposite the right angle and the longest side.

• The side adjacent to the right angle.

When can the HL theorem be used?

• In isosceles triangles.

• In any triangle.

• In equilateral triangles.

• Only in right triangles.

Why can't SSA be used to prove triangle congruence?

• Because it requires three angles to be congruent.

• Because the third side does not have to be congruent.

• Because it only works for right triangles.

• Because it requires three sides to be congruent.

Tags

CCSS.8.G.A.2

What does the reflexive property state?

• A side or angle is congruent to its corresponding part in another triangle.

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

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

• A side or angle is congruent to itself.

Tags

CCSS.HSG.CO.B.7

What are vertical angles?

• Angles that are adjacent to each other.

• Angles that are opposite each other when two lines intersect.

• Angles that are on opposite sides of a transversal.

• Angles that are on the same side of a transversal.

Tags

CCSS.7.G.B.5

What angle relationship is created when a 'Z' shape is formed by parallel lines and a transversal?

• Alternate exterior angles

• Vertical angles

• Alternate interior angles

• Corresponding angles

Tags

CCSS.8.G.A.5