Concept explainers
a.
The converse, the inverse and the contrapositive of the given statement.
a.
Answer to Problem 8PSB
Converse: “If a ray divides an angle into two congruent
Inverse: “If a ray does not bisects an angle, then it does not divide the angle into two congruent lines.”
Contrapositive: “If a ray does not divide an angle into two congruent angles, then it does not bisect the angle.”
Explanation of Solution
Given information:
The sentence is “If a ray bisects an angle, it divides the angle into two congruent angles.”
Every conditional statement “If p, then q” has three other statements associated with it.
A converse (If q, then p)
An inverse
A contrapositive
By referring to above associated statements, we can write the converse, the inverse and the contrapositive of a statement.
b.
The converse, inverse, and contrapositive of “If two sides of a
b.
Answer to Problem 8PSB
Converse: “If two angles of a triangle are congruent, then sides opposite to those angles are congruent.”
Inverse: “If two sides of a triangle are not congruent, then the angles opposite to those sides are not congruent.”
Contrapositive: “If two angles of a triangle are not congruent angles, then the sides opposite to those angles are not congruent.”
Explanation of Solution
Given information:
The given sentence is “If two sides of a triangle are congruent, then angles opposite to those sides are congruent.”
Every conditional statement “If p, then q” has three other statements associated with it.
A converse (If q, then p)
An inverse
A contrapositive
By referring to above associated statements, we can write the converse, the inverse and the contrapositive of a statement.
Chapter 1 Solutions
Geometry For Enjoyment And Challenge
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