Right Triangle Congruence Theorems Explained

The video tutorial covers the application of right triangle congruence theorems, including leg angle, hypotenuse angle, and leg leg theorems. It provides step-by-step proofs for triangle congruence and demonstrates practical applications, such as designing a plastic cover to fit metal plates. The tutorial emphasizes the simplicity of proving congruence by focusing on right triangles and congruent parts.

What is the main focus of the lesson practice in this video?

• Proving that two triangles are similar

• Proving that two triangles are congruent

• Finding the area of right triangles

• Calculating the perimeter of right triangles

Which theorem is used to prove that triangle ABC is congruent to triangle DF when AB is congruent to DE and angle A is congruent to angle D?

• Leg-Angle (LA) Theorem

• Leg-Leg (LL) Theorem

• Hypotenuse-Angle (HA) Theorem

• Angle-Side-Angle (ASA) Theorem

What additional information is needed to prove that triangles ABC and DF are right triangles?

• The triangles have equal hypotenuses

• The triangles have equal areas

• The triangles have a right angle

• The triangles have equal perimeters

When using the Hypotenuse-Angle (HA) theorem, which parts of the triangles must be congruent?

• Two legs

• Two angles

• A leg and an angle

• The hypotenuse and an angle

In the Hypotenuse-Angle (HA) theorem, what is the significance of the hypotenuse?

• It is the side opposite the smallest angle

• It is the side adjacent to the right angle

• It is the shortest side of the triangle

• It is the longest side of the triangle

Which theorem is used to prove triangle congruence when AB is congruent to DE and BC is congruent to EF?

• Side-Side-Side (SSS) Theorem

• Leg-Leg (LL) Theorem

• Hypotenuse-Angle (HA) Theorem

• Leg-Angle (LA) Theorem

What must be true about the sides AB and DE, and BC and EF, to use the Leg-Leg (LL) theorem?

• They must be the hypotenuses

• They must be the legs

• They must be the perimeters

• They must be the angles

In the practical example, what dimensions does Rachel need to ensure the plastic cover fits the metal plate?

• Two angles

• Two sides

• One side and the perimeter

• One angle and one side

If Rachel provides P = 14.2 cm and QR = 8.9 cm, which theorem proves the cover will fit the plate?

• Hypotenuse-Leg (HL) Theorem

• Leg-Angle (LA) Theorem

• Hypotenuse-Angle (HA) Theorem

• Leg-Leg (LL) Theorem

What is the key concept behind the Hypotenuse-Leg (HL) theorem?

• The hypotenuse and one angle must be congruent

• Two legs must be congruent

• Two angles must be congruent

• The hypotenuse and one leg must be congruent