Question

→ Q. In the given figure, C is the midpoint of AB , D is the midpoint of XY and AC = XD. Using an Euclid's axiom , prove that AB = XY ←

Answer 1

While Solving this question, we will use two Euclid's axiom here.

Euclid's Axiom 6 : Things which are double of the same thing are equal to one another.

Euclid's Axiom 7 : Things which are halves of the same thing are equal to one another.

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Question : In the given figure, C is the midpoint of AB , D is the midpoint of XY and AC = XD. Using an Euclid's axiom , prove that AB = XY.

Solution :

We have ;

AB = 2AC      [ ∴ C is the midpoint of AB ]

XY = 2 XD     [ ∴ D is the midpoint of XY ]

Now,

AC = XD       [ Given ]

⇒ 2AC = 2nd    [ by Euclid's axiom 6 ]

⇒ AB = XY       [ by Euclid's axiom 7 ]

Hence, AB = XY

Answer 2

✋hlw sissy ✋

since,AC=XD

Euclid's Axion is ⤵⤵

↪If halves of two things are equal,the numbers are equal↩

so,Tø PrøØf→AB=XY

↪Proof↩

↪AC=XD...given


⭐AC=½AB⭐...mid point..( 1 )
⭐XD=½XY⭐...mid point..( 2 )

from 1) and 2)

↪½AB=½XY↩
↪AB=XY↩....⚠½ gets càncèllèd⚠

↪⭐Hèn¢è PrøVèD⭐↩