Question

11. The given figure shows a right AABC which is right-angled at B. BD AC and AB = BC = 10 cm. What is the length of AD?
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Answer 1

Answer:

In △ABD and △ABC we have  BD=BC

AB=AB [Common]   

∠ABD=∠ABC=90∘

∴ By SAS criterion of congruence we get   

△ABD≅△ABC  

⇒AD=AC and ∠DAB=∠CAB [By CPCT]  

⇒AD=AC and ∠DAB=x [∴∠CAB=x]   

Now, ∠DAC=∠DAB+∠CAB=x+x=2x

∴∠DAC=∠ACD

⇒DC=AD [Side Opposite to equal angles]

⇒2BC=AD since DC=2BC

⇒2BC=AC Since AD=AC

Hence proved.