Q. ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then angle A and angle B respectively are what?

Asked by abbu786 | 28th Sep, 2017, 03:22: PM

Expert Answer:

begin mathsize 16px style In space triangle AED space and space triangle BED comma
AE equals BE thin space space space space left parenthesis DE space bisects space AB right parenthesis
angle AED equals angle BED space space space space space left parenthesis Each space right space angle right parenthesis
DE equals DE space space space space space space space left parenthesis common right parenthesis
therefore space space triangle AED space approximately equal to triangle BED space space space space space left parenthesis SAS space congruence right parenthesis
rightwards double arrow AD equals BD space space space space space left parenthesis CPCT right parenthesis
But thin space AD equals AB space space space space space left parenthesis Sides space of space straight a space rhombus space are space equal right parenthesis
rightwards double arrow AD equals AB equals BD
rightwards double arrow triangle ABD space is space an space equilateral space triangle.
rightwards double arrow angle straight A equals 60 degree
Now comma space angle straight A equals angle straight C equals 60 degree space space space space left parenthesis Opposite space angles space of space thin space rhombus space are space equal right parenthesis
Sum space space of space adjacent space angles space of space straight a space rhombus space are space supplementary.
rightwards double arrow angle ABC plus angle BCD equals 180 degree
rightwards double arrow angle ABC equals 120 degree
Hence comma space angle straight A equals 60 degree space and space angle straight B equals 120 degree
end style
 

Answered by Rashmi Khot | 29th Sep, 2017, 12:53: PM