Mathematics

Grade9

Easy

Question

# Arrange statements A–E

Write an indirect proof of the corollary:

If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.

Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.

A. That means say ∠R or ∠Q is a right angle.

B. But this contradicts, the given statement that QR is the hypotenuse.

C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.

D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.

E. Temporarily assume that ∠P is not a right angle.

What is the last statement of proof?

- A
- B
- C
- D

## The correct answer is: C

### The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.

### Related Questions to study

Mathematics

### Arrange statements A–E

Write an indirect proof of the corollary:

If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.

Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.

A. That means say ∠R or ∠Q is a right angle.

B. But this contradicts, the given statement that QR is the hypotenuse.

C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.

D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.

E. Temporarily assume that ∠P is not a right angle.

What is the third statement of proof?

### Arrange statements A–E

Write an indirect proof of the corollary:

If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.

Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.

A. That means say ∠R or ∠Q is a right angle.

B. But this contradicts, the given statement that QR is the hypotenuse.

C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.

D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.

E. Temporarily assume that ∠P is not a right angle.

What is the third statement of proof?

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### Arrange statements A–E

Write an indirect proof of the corollary:

If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.

Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.

A. That means say ∠R or ∠Q is a right angle.

B. But this contradicts, the given statement that QR is the hypotenuse.

C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.

D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.

E. Temporarily assume that ∠P is not a right angle.

What is the first statement of proof?

### Arrange statements A–E

Write an indirect proof of the corollary:

If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.

Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.

A. That means say ∠R or ∠Q is a right angle.

B. But this contradicts, the given statement that QR is the hypotenuse.

C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.

D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.

E. Temporarily assume that ∠P is not a right angle.

What is the first statement of proof?

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