Hypotenuse-Leg Congruence

Front

What is the Hypotenuse-Leg Congruence Theorem?

Back

The Hypotenuse-Leg Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

What is a hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is a leg in a right triangle?

Back

A leg in a right triangle refers to either of the two sides that form the right angle.

Front

How do you determine if two triangles are congruent using the Hypotenuse-Leg Theorem?

Back

To determine if two triangles are congruent using the Hypotenuse-Leg Theorem, check if the hypotenuses are equal and if one corresponding leg is equal.

Front

If triangle ABC has a hypotenuse of 10 cm and one leg of 6 cm, and triangle DEF has a hypotenuse of 10 cm and one leg of 6 cm, are the triangles congruent?

Back

Yes, triangle ABC and triangle DEF are congruent by the Hypotenuse-Leg Theorem.

Front

What is the formula for finding the length of the hypotenuse in a right triangle?

Back

The length of the hypotenuse can be found using the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the legs.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

Can the Hypotenuse-Leg Theorem be used for non-right triangles?

Back

No, the Hypotenuse-Leg Theorem is specific to right triangles.

Front

What is the significance of congruence in geometry?

Back

Congruence in geometry indicates that two figures are identical in shape and size, allowing for the application of various geometric principles.

Front

What is an example of a real-world application of the Hypotenuse-Leg Theorem?

Back

An example is in construction, where ensuring that two triangular supports are congruent can provide stability to a structure.