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Question
In the figure below, if AC>AB and D is point on AC such that AB = AD, then which of the following relation is true between BC and CD?
In the figure below, if AC>AB and D is point on AC such that AB = AD, then which of the following relation is true between BC and CD?
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Solution
The correct option is B BC > CD
In △ABC,
Theorem: Sum of lengths of any two sides of a triangle is always more than the length of the third side.
On using the above theorem;
AB + BC > AC
⇒ AB + BC > AD + CD (Since AC = AD + DC)
⇒ AB + BC > AB + CD (Since AB = AD)
⇒ BC > CD
In △ABC,
Theorem: Sum of lengths of any two sides of a triangle is always more than the length of the third side.
On using the above theorem;
AB + BC > AC
⇒ AB + BC > AD + CD (Since AC = AD + DC)
⇒ AB + BC > AB + CD (Since AB = AD)
⇒ BC > CD
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