Triangle Congruence Tests and Proofs

The video tutorial explains four tests to determine if two triangles are congruent: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Right Angle-Hypotenuse-Side (RHS). Each test is described with conditions that must be met for triangles to be congruent. The tutorial includes examples and a step-by-step guide on writing proofs for congruent triangles, emphasizing the importance of providing reasons for each step.

What is the primary purpose of congruent triangle tests?

• To determine if two triangles are similar

• To prove that two triangles are congruent

• To calculate the area of triangles

• To find the perimeter of triangles

Which of the following is NOT a congruent triangle test?

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Angle (AAA)

What does the SSS test require to prove triangle congruence?

• Two sides and an angle

• One side and two angles

• Three sides

• Two angles and a side

In the SSS test, what must be true about the sides of the triangles?

• One side must be equal

• Two sides must be equal

• All three sides must be equal

• No sides need to be equal

What is the key feature of the SAS test?

• Two angles and a side

• One side and two angles

• Three sides

• Two sides and the included angle

In the SAS test, where is the angle located?

• At the end of the two sides

• It doesn't matter

• In the middle of the two sides

• At the beginning of the two sides

What does the ASA test require for triangle congruence?

• Two angles and a side

• Three sides

• Two sides and an angle

• One angle and two sides

In the ASA test, what must be true about the angles?

• They must be adjacent

• They must be opposite

• They must be equal

• They must be supplementary

What is unique about the RHS test?

• It applies to all triangles

• It applies only to right-angled triangles

• It requires three equal sides

• It requires two equal angles

In the RHS test, what must be true about the hypotenuse?

• It must be perpendicular to the base

• It must be shorter than the other sides

• It must be equal in both triangles

• It must be longer than the other sides