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Maths-

General

Easy

Question

In $capital delta$ ABC , $angle$ B = 70° , $angle$ C = 40° , D is s point on BC and AB = AD. Then

AB > CD
AB = CD
AB < CD
cannot decide

The correct answer is: AB > CD

$I n space t r i a n g l e space A B C angle A B C plus angle A C B plus angle B A C equals 180 space left parenthesis a n g l e space s u m space p r o p e r t y space o f space t r i n g l e right parenthesis 70 plus 40 plus angle B A C equals 180 space angle B A C equals 180 minus 110 angle B A C equals 70 space... left parenthesis i right parenthesis I n space t r i a n g l e space A B D A B equals A D t h e r e f o r e space angle A B D equals angle A D B space left parenthesis a n g l e s space f o r m e d space b y space e q u a l space s i d e s space o f space t r i a n g l e space a r e space a l s o space e q u a l right parenthesis angle A D B equals 70 a l s o angle A B D plus angle A D B plus angle D A B equals 180 space left parenthesis a n g l e space s u m space p r o p e r t y right parenthesis 70 plus 70 plus angle D A B equals 180 angle D A B equals 180 minus 140 angle D A B equals 40 I n space t r i a n g l e space A C D angle D A C equals angle B A C minus angle D A B angle D A C equals 70 minus 40 angle D A C equals 30 a l s o angle A D C plus angle A C D plus angle D A C equals 180 30 plus 40 plus angle A D C equals 180 angle A D C equals 180 minus 70 angle A D C equals 110 W e space c a n space n o t space f i n d space a n y space r e l a t i o n s h i p space b e t w e e n space A B space a n d space C D S o space w e space c a n n o t space d e c i d e$

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