Solve the equation x -15 = 25 and state Euclid's Axiom used here.

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(a)

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

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

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In the given figure, it is given that \(\angle \)1 = \(\angle \)4 and \(\angle \)3 = \(\angle \)2. By which Euclid's axiom, it can be shown that if \(\angle \)2 = \(\angle \)4, then \(\angle \)1 = \(\angle \)3.

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

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(i) If a point C lies between two points A and B such that AC = BC, then prove that  AC=  AB.
(ii) Is CB = \(1\over2\)  AB?
(iii) Apala says that the ratio of AC and BC is 1 : 1. Is she correct? If so, which value of Apala is depicted by her statement?
(iv) Which mathematical concept has been covered in this problem?
(v) Write the formulae used in the solution

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(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.

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(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.

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Using Euclid's axiom, Compare length AD and AF. State which axiom you used here. Aso give two more axiom other than the axiom used in the above situation.

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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?

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(a)