To show that point X is equidistant from points P and Q.
Answer to Problem 17PSC
Point X is equidistant from points P and Q.
Explanation of Solution
Given information:
A, X and B lie in plane m .
P and Q are above m .
B is at equal distance from P and Q.
A is at equal distance from P and Q.
Formula used:
The below properties are used:
Points distant from same point form congruent segments.
Two
Two triangles are congruent by SAS congruence rule.
Proof:
It is given that,
A, X and B lie in plane m .
P and Q are above m .
B is at equal distance from P and Q.
A is at equal distance from P and Q.
Points distant from same point form congruent segments.
By reflexive property, we get
By SSS congruence rule, we get
As corresponding parts of congruent triangles are congruent, we get
By reflexive property, we get
By SAS congruence rule, we get
As corresponding parts of congruent triangles are congruent, we get
According to definition of equal distance,
X is equal distance from P and Q.
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