Exploring Congruence in Right Triangles

Why is side-side-angle not a valid method to prove two triangles are congruent?

• It only works for isosceles triangles.

• It does not guarantee the angles are congruent.

• It only works for equilateral triangles.

• It does not guarantee the sides are congruent.

What is the hypotenuse in a right triangle?

• The shortest side of the triangle.

• The longest side of the triangle.

• The side opposite the right angle.

• The side adjacent to the right angle.

What does the hypotenuse-leg (HL) theorem state?

• If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another triangle, the triangles are congruent.

• If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are similar.

• If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another triangle, the triangles are similar.

• If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Which of the following is NOT a condition for the hypotenuse-leg theorem?

• The hypotenuses of the triangles must be congruent.

• The triangles must be right triangles.

• The triangles must have one pair of congruent angles.

• The triangles must have one pair of congruent legs.

What is the first condition required for the hypotenuse-leg theorem?

• The triangles must have congruent hypotenuses.

• The triangles must have congruent angles.

• The triangles must be right triangles.

• The triangles must have one pair of congruent legs.

In the flow proof example, what does it mean when AB is perpendicular to BC?

• AB and BC are congruent.

• AB and BC form a right angle.

• AB and BC are bisected.

• AB and BC are parallel.

What is the definition of a bisector in the context of the flow proof example?

• A line that is parallel to another line.

• A line that divides an angle into two equal parts.

• A line that divides a segment into two equal parts.

• A line that is perpendicular to another line.

In the flow proof example, why are AC and CD congruent?

• Because AB is perpendicular to BC.

• Because DE is perpendicular to EC.

• Because B bisects AD.

• Because AB is congruent to DE.

What is the final step in the flow proof example to prove the triangles are congruent?

• Show that the right angles are congruent.

• Use the hypotenuse-leg theorem.

• Show that the legs are congruent.

• Show that the hypotenuses are congruent.

Why is the hypotenuse-leg theorem important in proving triangle congruence?

• It is the only method to prove congruence for isosceles triangles.

• It provides a method to prove congruence for right triangles.

• It works for all types of triangles.

• It is the simplest method to prove congruence for all triangles.