Exploring Triangle Congruence Theorems

The video tutorial covers the application of various theorems to prove triangle congruence, including angle-side-angle and side-angle-side criteria. It explains the use of the reflexive property and vertical angles to establish congruence. The tutorial provides examples and discusses how to identify missing information needed to prove congruence.

Which of the following is NOT a theorem used to prove triangle congruence?

• Side-Angle-Side

• Angle-Angle-Side

• Angle-Side-Angle

• Angle-Side-Side

What additional properties can be used to prove triangle congruence besides the marked information?

• Parallel lines and corresponding angles

• Supplementary angles and the associative property

• Vertical angles and the reflexive property

• Alternate interior angles and the transitive property

In the first example, why can't the triangles be proven congruent?

• They do not have any congruent sides.

• They do not have any congruent angles.

• The non-included angle and two sides do not form a valid congruence theorem.

• The triangles are not right triangles.

Which theorem is used to prove the triangles congruent in the second example?

• Angle-Side-Angle

• Side-Side-Side

• Hypotenuse-Leg

• Angle-Angle-Side

In the third example, which property is used to show that the shared side is congruent?

• Transitive property

• Symmetric property

• Vertical angles

• Reflexive property

What additional information is needed to prove the triangles congruent in the fourth example?

• The hypotenuse of the triangles

• The vertical angles

• The included angle between two sides

• The non-included side

In the fifth example, which theorem is used to prove the triangles congruent?

• Angle-Side-Angle

• Side-Side-Side

• Hypotenuse-Leg

• Angle-Angle-Side

What is the missing piece of information needed to prove the triangles congruent in the sixth example?

• The included angle between two sides

• The hypotenuse of the triangles

• The vertical angles

• The non-included side

In the seventh example, which side needs to be congruent to prove the triangles congruent?

• BC and AD

• CA and JL

• AB and CD

• DE and FG

In the eighth example, which angle needs to be congruent to prove the triangles congruent?

• Angle D and Angle KJ

• Angle A and Angle B

• Angle C and Angle D

• Angle E and Angle F