The number of line segments determined by three collinear points is:

Two planes intersect each other to form a:

The thing which coincide with one another are:

How many lines can be passed through two distinct points?

Write the number of dimension(s) of a surface.

In the given figure, we have AB=AD and AC=AD. Prove that AB=AC. State the Euclid's axiom to support this.

Solve the equation x+4=10 and state Euclid's axiom used.

In a triangle PQR, X and Y are the points on PQ are QR respectively. If PQ = QR and QX = QY, Show that PX = RY.

In figure, AE = DF, E is the mid-point of AB and F is the mid-point of DC. Using an Euclid's axiom, show that AB = DC.

Prove that every line segment has one and only one mid-point.

Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them?
(i) parallel lines  
(ii) perpendicular lines
(iii) line segment
(iv) radius of a circle
(v) square.

In figure, if AC = BD, then prove that AB = CD.

Does Euclid 's fifth postulate simply the existence of parallel lines? Explain.

In a triangle ABC, X and Y are the points On AB and BC such that BX = BY and AB = BC. Show that AX = CY. State the Euclid's Axiom used.

In the given figure, we have \(\angle1=\angle3\) and \(\angle2=\angle4\). Show that, \(\angle A=\angle C.\)

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

(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

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.

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.

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?