Question

Q. IN THE GIVEN FIGURE WE HAVE X AND Y ARE THE MIDPOINTS OF AB AND BC RESPECTIVELY AND AX= CY. SHOW THAT AB=BC.

Answer 1

Answer on Question #69290 – Math – Geometry

Question

IN THE GIVEN FIGURE WE HAVE X AND Y ARE THE MIDPOINTS OF AB AND BC RESPECTIVELY AND AX= CY. SHOW THAT AB=BC.

Solution

We have

$$AX = CY \text{ (given)};$$ $$BX = AX \text{ ( } X \text{ is the midpoint of } AB \text{ )};$$ $$CY = BY \text{ ( } Y \text{ is the midpoint of } BC \text{ )}.$$

Then

$$BX = AX = CY = BY.$$

So

$$BX = BY.$$

The Euclid axiom (second axiom): If equals be added to the equals, the wholes are equal.

Thus,

$$AX + BX = CY + BY = BY + CY,$$

hence

$$AB = BC.$$

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