(a)
To Prove: The paragraph proof for the given data.
(a)
Explanation of Solution
Given:
The lines l and m intersect at the point p. A is any point that is no on l or m.
The objective is to prove that if you reflect A in m, and the reflect its image
Calculation:
By the definition of the reflection the m is the perpendicular bisector of
As the two points form one line than the auxiliary segments are,
As, the perpendicular bisector is the line segment that divides the two equal parts then,
Then, use reflective property as,
Then, use SAS congruence as,
Then, by CPCTC
Hence, the rotation moves every point of the pre-image with the specified angle and the direction about the fixed point. Then,
Hence, proved.
(b)
To Prove: The paragraph proof for the given data.
(b)
Explanation of Solution
Given:
The lines l and m intersect at the point p. A is any point that is no on l or m.
The objective is to prove
Calculation:
Consider that the congruent segment are those that are equal in length as,
Then, by addition postulate,
Then, by substitution,
Hence, Proved.
Chapter 9 Solutions
Geometry, Student Edition
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