Medium
If a point $C$ lies between two points $A$ and $B$ such that $AC = BC$,then prove that $AC = \frac{1}{2} AB$. Explain by drawing the figure.
(N/A) Given: Point $C$ lies between $A$ and $B$ such that $AC = BC$.
To prove: $AC = \frac{1}{2} AB$.
Proof:
Since $C$ lies between $A$ and $B$,we have $AC + BC = AB$.
Given that $AC = BC$.
Substituting $AC$ for $BC$ in the equation $AC + BC = AB$,we get:
$AC + AC = AB$
$2 AC = AB$
Dividing both sides by $2$,we get:
$AC = \frac{1}{2} AB$.
Hence proved.
To prove: $AC = \frac{1}{2} AB$.
Proof:
Since $C$ lies between $A$ and $B$,we have $AC + BC = AB$.
Given that $AC = BC$.
Substituting $AC$ for $BC$ in the equation $AC + BC = AB$,we get:
$AC + AC = AB$
$2 AC = AB$
Dividing both sides by $2$,we get:
$AC = \frac{1}{2} AB$.
Hence proved.
Explore More
Similar Questions
Does Euclid's fifth postulate imply the existence of parallel lines? Explain.
Medium
View SolutionConsider two 'postulates' given below:
$(i)$ Given any two distinct points $A$ and $B$,there exists a third point $C$ which is in between $A$ and $B$.
$(ii)$ There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid's postulates? Explain.
$(i)$ Given any two distinct points $A$ and $B$,there exists a third point $C$ which is in between $A$ and $B$.
$(ii)$ There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid's postulates? Explain.
Medium
View SolutionProve that an equilateral triangle can be constructed on any given line segment.
Medium
View SolutionGive a definition for square terms. Are there other terms that need to be defined first? What are they,and how might you define them?
Medium
View SolutionGive a definition for the term 'line segment'. Are there other terms that need to be defined first? What are they,and how might you define them?
Difficult
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo