Triangle Congruence Proofs: SSS and HL Techniques

This video tutorial covers methods of proving triangle congruence using the side-side-side (SSS) and hypotenuse-leg (HL) theorems. It provides a proof checklist and tips for effectively proving congruence, including handling shared sides and different orientations. Two examples are worked through: one using the SSS theorem and another using the HL theorem, demonstrating the application of these concepts in geometric proofs.

What are the two main theorems discussed in the video for proving triangle congruence?

• Angle-Side-Angle (ASA) and Hypotenuse-Leg (HL)

• Side-Side-Side (SSS) and Angle-Side-Angle (ASA)

• Side-Side-Side (SSS) and Hypotenuse-Leg (HL)

• Side-Angle-Side (SAS) and Angle-Side-Angle (ASA)

According to the Side-Side-Side (SSS) theorem, when are two triangles congruent?

• When all three angles of one triangle are equal to all three angles of another triangle

• When two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle

• When all three sides of one triangle are equal to the corresponding sides of another triangle

• When the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle

What must be true about a triangle to use the Hypotenuse-Leg (HL) theorem?

• It must have at least one angle greater than 90 degrees

• It must be an equilateral triangle

• It must be a right triangle

• It must be an isosceles triangle

What is the correct way to write the Hypotenuse-Leg (HL) theorem in a proof?

• Hypotenuse and Leg are congruent

• HL is congruent to HL

• HL is equal to HL

• Hypotenuse and Leg are equal

What should you do if triangles have a shared side or are overlapping?

• Ignore the shared side and focus on other sides

• Use the shared side as a base for comparison

• Separate the triangles and relabel them

• Rotate the triangles to match their orientation

What is the first step in the proof checklist?

• Come up with a game plan

• Label the given information on the diagram

• Make a statement and reason chart

• Identify the shared sides

In the example proof, what is the reason for stating that XM is congruent to YM?

• Given information

• Side-Side-Side theorem

• Reflexive property

• Definition of midpoint

What property is used when a side is shared between two triangles?

• Symmetric property

• Associative property

• Transitive property

• Reflexive property

What should you do if you get stuck while working on a proof?

• Start over from the beginning

• Ask for help

• Refer back to the proof checklist

• Skip to the next step

What is the final step in the proof checklist?

• Label the diagram

• Write the given information

• Make the final congruence statement

• Identify the shared sides