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Question

In a rhombus ABCD, the altitude from D to the side B bisects AB. Find the angles of the rhombus.
1715492_5c6681d389a54382b2a1dac817fac77a.png

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Solution

From the figure consider DP bisects the side AB at point P

Construct a line at BD

Consider AMD and BMD

We know that M is the midpoint of AB
AM=BM

from the figure we know that

AMD=BMD=90o

MD is common ie MD=MD

By SAS congruency criterion

AMDBMD

AD=BD (c.p.c.t)

We know that the sides of a rhombus are equal

so we get

AD=AB

It can be written as

AD=AB=BD

We know that ADB is an equilateral triangle

so we get

A=60o

we know that

B+A=180o

B=180oA

B=180o60o

B=120o

We know that D=B=120o

Therefore the angles are C=A=60o and D=B=120o

1565358_1715492_ans_06377874802c4ab4bbe61b996886960a.png

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