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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.
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
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,