# Lesson Worksheet: The Converse of the Pythagorean Theorem Mathematics • 8th Grade

In this worksheet, we will practice using the converse of the Pythagorean theorem to determine whether a triangle is a right triangle.

Q1:

What can the converse of the Pythagorean theorem be used for?

• Ademonstrating that a triangle is equilateral
• Bdemonstrating that a triangle has a right angle
• Cfinding the angles in a triangle
• Dfinding lengths in an equilateral triangle
• Edemonstrating that a triangle is an isosceles triangle

Q2:

Can the lengths 7.9 cm, 8.1 cm, and 5.3 cm form a right triangle?

• ANo
• BYes

Q3:

Is a right triangle at ? • AYes
• BNo

Q4:

A triangle has sides of lengths 36.4, 27.3 and 45.5. What is its area?

Q5:

The Pythagorean theorem states that, in a right triangle, the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. Does this mean that a triangle where is necessarily a right triangle?

Let us assume that is of side lengths , , and , with . Let be a right triangle of side lengths , , and . Using the Pythagorean theorem, what can you say about the relationship between , , and ?

• A
• B
• C

We know that for , .

What do you conclude about ?

• A
• B
• C

Is it possible to construct different triangles with the same length sides?

• ANo
• BYes

What do you conclude about ?

• AIt is similar to , so it has a right angle at .
• BIt is congruent to , so it has a right angle at .
• CIt is congruent to , so it has a right angle at .
• DIt is congruent to , so it has a right angle at .
• EIt is similar to , so it has a right angle at .

Q6:

In triangle , point lies on , , , , and . Find the length of to the nearest tenth, and then determine whether is a right triangle or not.

• A, a right triangle
• B, not a right triangle
• C, a right triangle
• D, not a right triangle

Q7:

In triangle , let on be the foot of the altitude from . If , , and , is right angled at ?

• ANo
• BYes

Q8:

In triangle , is perpendicular to , lies between and , , , and . Is a right triangle? • ANo
• BYes

Q9:

What does equal to? • A
• B
• C
• D

Q10:

In the figure shown, suppose that and . Determine and rounded to the nearest hundredth, if necessary. • A,
• B,
• C,
• D,

This lesson includes 10 additional questions and 90 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.