IXL - Hypotenuse-Leg Theorem (Geometry practice)

What values of

and

make

△

FGH

≅

△

TSR

ref_doc_title.

Learn with an example

question

What values of

and

make

△

EFG

≅

△

HIJ

key idea

The Hypotenuse-Leg Theorem states that two right triangles are congruent if and only if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of the other right triangle.

solution

Use the Hypotenuse-Leg Theorem to solve for the values of

and

that make the triangles congruent.

First, look at the labeled pair of corresponding legs. The first leg

has a length of

and the second leg

has a length of 16. For the triangles to be congruent, the leg lengths must be equal. So,

must equal 16.

Now, look at the hypotenuses. The first hypotenuse

has a length of 49 and the second hypotenuse

has a length of

For the triangles to be congruent, the hypotenuse lengths must be equal. So,

must equal 49.

The values of

and

that make

△

EFG

≅

△

HIJ

are

and

Looking for more? Try these:

Lesson: Congruence

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Teacher tools

Work it out

Not feeling ready yet? These can help:

K.2Solve problems involving corresponding parts

C.13Solve linear equations: mixed review

Lesson: Congruence

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