Concept explainers
a
To distinguish the statement “The acute
a
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
Thus, this statement is always true
b
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
b
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
Thus, this statement is always true
c
To distinguish the statement “A triangle contains two obtuse angles” in either of A, S or N
c
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
Thus the given statement is never true
d
To distinguish the statement “If one of the angles of an isosceles triangle is
d
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
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
Thus, the given statement is always true
e
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
e
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.
Chapter 7 Solutions
Geometry For Enjoyment And Challenge
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