A day full of math games & activities. Find one near you.

ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus.
Hint: Join BD. Then ∆ ABD is equilateral.

Solution:

Given, ABCD is a rhombus.

The perpendicular bisector of AB passes through D.

We have to find the angles of the rhombus.

ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus. Hint: Join BD. Then ∆ ABD is equilateral

DE is the altitude on AB.

Now, AE = EB.

Considering ΔAED and ΔBED,

Common side = DE

∠AED = ∠BED = 90°

Given, AE = EB

By SAS criterion, ΔAED ≅ ΔBED

By CPCT,

AD = BD ------------------- (1)

We know that all sides of a rhombus are equal.

So, AD = AB ------------- (2)

From (1) and (2),

AD = AB = BD

Since the three sides are equal, ABD is an equilateral triangle.

In an equilateral triangle, each angle is equal to 60 degrees.

So, ∠A = 60°

We know that the opposite angles of a rhombus are equal.

So, ∠A = ∠C = 60°

We know that the sum of adjacent angles of a rhombus is supplementary.

So, ∠ABC + ∠BCD = 180°

∠ABC + 60° = 180°

∠ABC = 120°

We know that the opposite angles of a rhombus are equal.

So, ∠ABC = ∠ADC = 120°

Therefore, the angles of rhombus are ∠A = ∠C = 60° and ∠B = ∠D = 120°.

✦ Try This: ABCD is parallelogram whose diagonals intersect at O. If OD = 9 cm,OB = x + y cm, OA = x - y, and OC = 5 cm, find x and y.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 179