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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:

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?

  • Ayes
  • Bno

What do you conclude about ?

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

Q2:

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

  • Afinding the angles in a triangle
  • Bfinding lengths in an equilateral triangle
  • Cdemonstrating that a triangle is equilateral
  • Ddemonstrating that a triangle has a right angle
  • Edemonstrating that a triangle is an isosceles triangle

Q3:

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

  • Ano
  • Byes

Q4:

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

  • Ano
  • Byes

Q5:

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

  • Ayes
  • Bno

Q6:

Is a right triangle at ?

  • Ano
  • Byes

Q7:

Is a right triangle at ?

  • Ayes
  • Bno

Q8:

Is a right triangle at ?

  • Ano
  • Byes

Q9:

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

Q10:

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 , not a right triangle
  • D , a right triangle

Q11:

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

Q12:

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

Q13:

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

Q14:

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

  • Ano
  • Byes

Q15:

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

  • Ayes
  • Bno

Q16:

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

  • Ano
  • Byes
  • Published