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  • Solve each of the following question using appropriate Euclid’s axiom: In the Fig.5.5, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

Solve each of the following question using appropriate Euclid’s axiom:  In the Fig.5.5, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

Answers (1)

Solution:

To prove: AC = BC

Here given that

AX = CY                                 … (1)

Here X is mid-point of AC

AX = CX =\frac{1}{2} AC

2AX = 2CX = AC                   … (2)

Also, Y is mid-point of BC

BY = CY =\frac{1}{2} BC

2BY = 2CY = BC                    … (3)

Euclid’s axiom says that things which are double of the same things are equal to one another.

Hence from equation (1, 2, 3)

2AX = 2CY

Implies AC = BC

Hence proved

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