In the given figure, if AB = CD, then prove that AC = BD. Also, write the Euclid's Axiom used for proving it.

5

(a)

In the given figure AB = BC and BX = BY. Show that AX = CY. State Euclid's Axiom used.

5

(a)

In figure, C is the mid-point of AB and Dis the mid-point of AC. Prove that AD = \(1\over2\)  AB.

5

(a)

In the fig, we have \(\angle1=\angle3 \ and\ \angle2=\angle4.\) Show that \(\angle A= \angle C.\) State which axiom you use here. Also give two more axioms other than the axioms used in the above situation.

5

(a)

In the fig., if \(OX=\frac{1}{2}XY,\ PX=\frac{1}{2}XZ\) and OX = PX, Show that XY = XZ. State which axiom you use here. Also give two more axioms other than the oxiom used in the above situation.

5

(a)

Read the following statement :
"A square is a polygon made up of four line segments, out of which, length of three line segement, out of which length of three line segments are equal to the length of fourth one and all its angles are right angles."
(i) Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all angles and sides of a square are equal?
(iii) What is its value?

5

(a)