Introduction to Euclid's Geometry
CBSE Most Repeated PYQs

Euclid's Axiom 1: Things which are equal to the same thing are equal to one another.

A solid has 3 dimensions (length, breadth, height).

A point has zero dimensions (no length, breadth or height).

The boundaries of solids are surfaces.

Euclid's Axiom 2. Both A and R are true.

Both statements are true Euclid's postulates/axioms, but R does not explain A.

AC + BC = AB. Since AC = BC, AC + AC = AB ⇒ 2AC = AB ⇒ AC = 1/2 AB.

If a straight line falling on two straight lines makes interior angles on same side less than two right angles, lines will meet on that side.

AC = AB + BC, BD = BC + CD. AB + BC = BC + CD ⇒ Subtracting BC gives AB = CD.

It holds true for all quantities in any field of science, nature and mathematics.

Through a single point, infinitely many lines can be drawn in all directions.

Draw circle with center A & radius AB, and circle with center B & radius AB. Intersection C gives AC = AB = BC.

Suppose D is another midpoint ⇒ AD = 1/2 AB. AC = AD ⇒ C and D coincide.

1. Equal to same thing are equal. 2. Equals added to equals are equal. 3. Equals subtracted are equal. 4. Coincide are equal. 5. Whole greater than part.

1. Straight line from any point to any point. 2. Terminated line produced indefinitely. 3. Circle with any center & radius. 4. All right angles equal. 5. Interior angles sum postulate.

AC + BC = AB. 15 + 15 = 30 m by Euclid's Axiom 2.

Since interior angles sum to 2 right angles (180°), lines will never intersect on either side, hence parallel.

AC coincides with AB + BC. Things which coincide with one another are equal to one another (Axiom 4).

AC = 1/2 AB = 5 cm. AD = 1/2 AC = 2.5 cm.

Suppose two lines have two common points P and Q. Then two distinct lines pass through P and Q, contradicting Postulate 1.