Triangle Congruence Theorems: SSS and SAS Explained

This video tutorial covers the concepts of triangle congruence, focusing on the Side-Side-Side (SSS) and Side-Angle-Side (SAS) theorems. It explains how to prove triangles are congruent using these theorems and provides examples of proofs. The importance of order in naming congruent triangles is emphasized, and the video also discusses the reflexive property, midpoint theorem, and alternate interior angles theorem as tools for proving congruence.

What does the Side-Side-Side (SSS) theorem state?

• Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

• Two triangles are congruent if all three angles of one triangle are congruent to all three angles of another triangle.

• Two triangles are congruent if one side and two angles of one triangle are congruent to one side and two angles of another triangle.

• Two triangles are congruent if all three sides of one triangle are congruent to all three sides of another triangle.

Why is the order of vertices important in triangle congruence?

• It helps in identifying the type of triangle.

• It is used to calculate the area of the triangles.

• It ensures that corresponding parts of the triangles are matched correctly.

• It determines the size of the triangles.

In the given proof, what property is used to state that segment FH is congruent to segment FH?

• Vertical Angles Theorem

• Reflexive Property

• Definition of a Segment Bisector

• Midpoint Theorem

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

• Two triangles are congruent if all three sides of one triangle are congruent to all three sides of another triangle.

• Two triangles are congruent if all three angles of one triangle are congruent to all three angles of another triangle.

• Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

• Two triangles are congruent if one side and two angles of one triangle are congruent to one side and two angles of another triangle.

What is an included angle in the context of the SAS theorem?

• An angle that is equal to 90 degrees.

• An angle that is supplementary to the other angles.

• An angle that is not between the two sides being considered.

• An angle that is between the two sides being considered.

In the proof involving the bow tie shape, which theorem is used to state that angle BCA is congruent to angle ECD?

• Alternate Interior Angles Theorem

• Vertical Angles Theorem

• Midpoint Theorem

• Reflexive Property

What property is used to state that segment GJ is congruent to segment GJ in the proof involving parallel lines?

• Midpoint Theorem

• Definition of a Segment Bisector

• Reflexive Property

• Vertical Angles Theorem

When two segments are perpendicular, what can be said about the angles formed?

• They are congruent to each other.

• They are supplementary.

• They are right angles.

• They are complementary.

What does the definition of an angle bisector state?

• It creates two supplementary angles.

• It creates two right angles.

• It divides a segment into two congruent segments.

• It divides an angle into two congruent angles.

In the final proof, what property is used to state that segment QS is congruent to segment QS?

• Midpoint Theorem

• Definition of a Segment Bisector

• Vertical Angles Theorem

• Reflexive Property