State whether the following statements are true or false? Also give reasons for your answers.

a) Only one line can pass through a given point.

b) All right angles are equal.

c) Circles with same radii are equal.

d) A finite line can be extended on its both sides endlessly to get a straight line.

e) From the figure, AB > AC

a) False

It is false because through a given point, infinite number of lines can pass.

b) True

Let us consider ∠ABC = 90°, ∠DEF = 90° and ∠GHI = 90°.

Here, ∠ABC = ∠DEF = ∠GHI

i.e. all the right angles are equal (By Postulate 4).

c) True

Two circles coincide if we superimpose the region bounded by one circle on the other circle. Then, their centers and boundaries also coincide.

∴ Circle with same radii will be equal.

d) True

It is true by Euclid’s postulate 2.

e) True

C is the midpoint of line segment AB dividing the lines into two halves i.e. AC = BC

⇒ AB = AC + BC

∴ AB > AC