Question

on a line ab tak four point P Q R and S in order such that PQ is equal to Rs state whether they are congruent QS give reason in support of your answer

Answer 1

Answer:

PQ = RS

A P Q R S B

<-----x------><------y------><-----x----->

Let's say PQ = RS =x

and QR = y

PR = PQ + OR

PR = x + y

QS = QR+RS

QS = y + x

QS = x + y

QS = PR

PR = QS

Hence PR congruent to QS

Answer 2

Given Question :-

On a line AB, take four point P, Q, R and S in order such that PQ is equal to RS. State whether they are congruent to QS. Give reason in support of your answer.

$\large\underline{\sf{Given- }}$

P, Q, R and S are four points on AB taken in order such that PQ = RS

$\large\underline{\sf{To\:state - }}$

Is it true PQ = RS = QS ?

$\large\underline{\sf{Solution-}}$

As it is given that, P, Q, R and S are the points on AB taken in order and PQ = RS

We know, From Euclid Lemma, part is smaller than the whole.

Now, From given data, we concluded that RS is a part of QS

$\rm\implies \:RS < QS$

$\rm\implies \:RS \: \ne \: QS$

$\rm\implies \:PQ \: \ne \: QS$

So,

$\rm\implies \:PQ \: = \: RS \: \ne \: QS$

Hence, Given statement is not true.

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ADDITIONAL INFORMATION

1. Every line segment has a finite length.

2. Two lines are congruent iff they have equal lengths.

3. A line contains infinitely many points.

4. Equal added to equals are equal.

5. Equal subtracted from equals are equal.

6. Whole is greater than the part.