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Question

ABCD is a rhombus in which the altitude from D to side AB bisects AB. Find the angles of the rhombus.  [4 MARKS]


Solution

Concept: 2 Marks
Application: 2 Marks

Let DL be the altitude from D on side AB. It is given that L bisects AB i.e.

AL = BL. Join points B and D to form diagonal BD.
In Δ ADL and ΔBDL,

DL = DL        [Common side]
ALD=BLD=90 [Given]
AL = BL  [Given]

So, by SAS congruence criterion,
ΔADLΔBDL
AD=BD

Since all sides of a rhombus are equal in length,
AD=CD=BC=AB=BD
ABD and BCD are equilateral.

A=C=60

ABC=ABD+DBC=60+60=120
ADC=ABC=120   [Opposite angles of a parallelogram are equal.] 

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