Question

15.
1 po
In right
2x
с
B
D
triangle ABC, right angled at B, angle
ACB is twice angle CAB (as shown in
the figure). If BC=2 cm, then hypotenuse
AC is equal to
3 cm
4 cm
O5 cm
6 cm
1 point
Time remaining: 00:19
р​

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.