Worksheet: The Converse of the Pythagorean Theorem

In this worksheet, you will be able to practice using the converse of the Pythagorean theorem to verify whether a triangle is a right triangle given its side lengths and also practice the means of identifying its right angle as well as finding its area.

Q1:

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

Ano
Byes

Q2:

Can the lengths 16.6 cm, 6.3 cm, and 11.3 cm form a right triangle?

Ano
Byes

Q3:

Can the lengths 14.4 cm, 19.2 cm, and 24 cm form a right triangle?

Ayes
Bno

Q4:

Is a right triangle at ?

Ano
Byes

Q5:

Is a right triangle at ?

Ayes
Bno

Q6:

Is a right triangle at ?

Ano
Byes

Q7:

In triangle point lies on and , , , 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

Q8:

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

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

Q9:

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

Q10:

A triangle has sides of lengths 20.4, 59.5 and 62.9. What is its area?

Q11:

A triangle has sides of lengths 44, 4.2 and 44.2. What is its area?

Q12:

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

Ano
Byes

Q13:

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

Ayes
Bno

Q14:

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

Ano
Byes

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