Q18 of 22 Page 5

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

From the figure,


AC = AB + BC


BD = BC + CD


AB + BC = BC + CD


According to Euclid’s axiom,


When two equals are subtracted from equals, remainders are also equal.


Subtracting BC both sides,


AB + BC – BC = BC + CD – BC


AB = CD


More from this chapter

All 22 →
16

In the Fig,

(i) AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC.
(ii) BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.


 17

If a point C lies between two points A and B such that AC = BC, then prove that AC = 1/2 AB. Explain by drawing the figure.

 19

A point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

 20

An equilateral triangle is a polygon made up of three-line segments out of which two-line segments are equal to the third one and all its angles are 60° each. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in an equilateral triangle?