Chapter 7.1, Problem 9PSA

a

To determine

To distinguish the statement “The acute angles of a right triangle are complementary” in either of A, S or N

Answer to Problem 9PSA

Final answer for the statement is A

Explanation of Solution

Given information:

The following statement has been given

The acute angles of a right triangle are complementary

We know that in any triangle, all the angles add up to ${180}^0$ . Given that one of the angles of a right triangle is ${90}^0$ , the other two become complementary to each other.

Thus, this statement is always true

b

To determine

To distinguish the statement “The supplement of one of the angles in a triangle is equal to he sum of the other two angles of the triangle” in either of A, S or N

Answer to Problem 9PSA

Final answer for the statement is A

Explanation of Solution

Given information:

The following statement has been given

The supplement of one of the angles in a triangle is equal to he sum of the other two angles of the triangle

We know that in any triangle, all the angles add up to ${180}^0$ . Thus, if we take supplement of one of the angles, the other two become equal to that value.

Thus, this statement is always true

c

To determine

To distinguish the statement “A triangle contains two obtuse angles” in either of A, S or N

Answer to Problem 9PSA

Final answer for the statement is N

Explanation of Solution

Given information:

The following statement has been given

A triangle contains two obtuse angles

We know that only for an obtuse angled triangle, only one of the angles can be obtuse. Otherwise the sum of the angles won’t be able to be ${180}^0$

Thus the given statement is never true

d

To determine

To distinguish the statement “If one of the angles of an isosceles triangle is ${60}^0$ , the triangle is equilateral” in either of A, S or N

Answer to Problem 9PSA

Final answer for the statement is A

Explanation of Solution

Given information:

The following statement has been given

If one of the angles of an isosceles triangle is ${60}^0$ , the triangle is equilateral

We know that in an isosceles triangle, the base angles are equal. Also, we know that the sum of the angles of any triangle has to be ${180}^0$ . Hence we can say that if one of the angles is ${60}^0$ , the other will be equal as well.

Thus, the given statement is always true

e

To determine

To distinguish the statement “If the sides of one triangle are doubled to form another triangle, each angle of the second triangle is twice as large the corresponding angle of first triangle” in either of A, S or N

Answer to Problem 9PSA

Final answer for the statement is N

Explanation of Solution

Given information:

The following statement has been given

If the sides of one triangle are doubled to form another triangle, each angle of the second triangle is twice as large the corresponding angle of first triangle.

We know that doubling the sides of any triangle will create a similar triangle. Thus, the sum of the angles will remain constant.