Q5 of 66 Page 106

In the given figure, it is given that AC=BD,

Prove that AB=CD.


From the above figure we get that,


AC = AB + BC


BD = BC + CD


And it is given is that AC = BD


So, AB + BC = BC + CD ………….(i)


According to Euclid’s axiom,when equals are subtracted from equals, the remainders are also equal.


Subtracting BC from both side in eq(i), we get


AB + BC − BC = BC + CD − BC


AB = CD


More from this chapter

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3

How many lines can be drawn to pass through

(A) a given point (B) two given points?

 4

A, B and C are three collinear points. How many line segments can be determined by them? Name these line segments.

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Show that every line segment has one and only one middle point.

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Define the following terms:

(A) Parallel lines (B) Intersecting lines


(C) Concurrent lines