Indirect Proofs - Practice 01

1. You want to write an indirect proof of the statement below. What should you first assume?
$\triangle ABC$ is not acute

$\triangle ABC$ is not acute

$\triangle ABC$ is equilateral

$\triangle ABC$ is obtuse

$\triangle ABC$ is acute

Question 1 of 10

2. You want to write an indirect proof of the statement below. What should you first assume?
$\triangle XYZ$ is scalene

$\triangle XYZ$ is scalene

$\triangle XYZ$ is obtuse

$\triangle XYZ$ is not scalene

$\triangle XYZ$ is equiangular

Question 2 of 10

3. What is the first step to this indirect proof?
$\angle A$ is obtuse

$\angle A$ is acute

$\angle A$ is not obtuse

$\angle A$ is more than $90 \textdegree$

$\angle A$ is obtuse

Question 3 of 10

4. You want to write an indirect proof of the statement below. What should you assume?

$\triangle CAR$ is not isosceles. Altitude $\overline{CD}$

Assume $\overline{CR}$ is congruent to $\overline{CD}$

Assume $\triangle CAR$ is isosceles

Assume $\overline{CD}$ bisects $\overline{AR}$

Assume $\overline{CD}$ is 5

Question 4 of 10

5. What is the reason for the given statement?
Perpendicular lines intersect at right angles

Perpendicular lines don't always form right angles

Step 1 is true

Definition of perpendicular lines

Perpendicular lines form obtuse angles

Question 5 of 10

6. What is the reason for the given statement?
The lengths 5in, 6in, and 7in don't form a triangle

Triangles have 3 sides

The hypotenuse is the longest side

The longest side of a triangle must be greater than the sum of the two shorter sides

The sum of two sides of a triangle must be greater than the third side

Question 6 of 10

7. Given that $\triangle RST$ is isosceles with vertex $R$ , prove that $\angle S \cong \angle T$ .
After stating the given information in the first step, which of the following is the second statement of the indirect proof?

$\angle S \cong \angle T$

$\angle S$ is not congruent to $\angle T$

$\overline{RS} \cong \overline{RT}$

Contradiction between statement 2 and 4

Question 7 of 10

8. Given that $\triangle RST$ is isosceles with vertex $R$ , prove that $\angle S \cong \angle T$ .
After stating the first two steps, which of the following is the third statement of the indirect proof?

$\angle S \cong \angle T$

$\angle S$ is not congruent to $\angle T$

$\overline{RS} \cong \overline{RT}$

Contradiction between statement 2 and 4

Question 8 of 10

9. Given that $\triangle RST$ is isosceles with vertex $R$ , prove that $\angle S \cong \angle T$ .
After stating the first three steps, which of the following is the fourth statement of the indirect proof?

$\angle S \cong \angle T$

$\angle S$ is not congruent to $\angle T$

$\overline{RS} \cong \overline{RT}$

Contradiction between statement 2 and 4

Question 9 of 10

10. Given that $\triangle RST$ is isosceles with vertex $R$ , prove that $\angle S \cong \angle T$ .
After stating the first four steps, which of the following is the fifth statement of the indirect proof?

$\angle S \cong \angle T$

$\angle S$ is not congruent to $\angle T$

$\overline{RS} \cong \overline{RT}$

Contradiction between statement 2 and 4

Question 10 of 10

Indirect Proofs – Practice 01