Question

In figure, AC = PQ and CP = BQ. Then P is the midpoint of the line segment AB.

A. True
B. False

Answer 1

Hint: In this question remember to use the given information to make the equations and also to approach towards the solution add the both L.H.S and R.H.S it will make this question easy for you.

Complete step by step solution:
According to the given information we have a line segment AB which consists of 5 points including its endpoint
Before approaching towards the solution let’s discuss what line segment is and what make line segments different from a straight line
A line segment is one of the type of line which have points more than 2 between the two ends of the line
Since here in this problem we have line segment with 5 points on it including its both ends but there is some relations given in the question between the points on the line segment that are
AC = PQ which means distance from point A to C is equal to distance from point P to Q
And CP = BQ which says that distance from C to P is equal to distance from B to Q
Adding the both L.H.S and both R.H.S of the given statement i.e. AC = PQ and CP = BQ
We get AC + CP = PQ + BQ (equation 1)
Since we know that AC + CP = AP and PQ + BQ = PB
Substituting the values in the equation 1
We get AP = PB
Since AP = PB thus it means P is the midpoint of line segment AB
Thus the statement is true
Hence option A is the correct option.

Note: In the above solution we used term line segments which is a type of line where line can be defined as a projection which is not bend or curved at any point from start point and end point of line this is called straight line the properties shown by straight lines are that a straight line have only one dimension it can be horizontal, diagonal or vertical in position, both ends of a straight line can be extend to an infinite distance and the sum of all the angles formed on line is equal to ${180^ \circ }$.