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Worksheet: The Converse of the Pythagorean Theorem
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
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
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
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