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# Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure

**Solution:**

ABCD is quadrilateral whose opposite angles are equal as shown below.

ABCD is a kite where ∠B = ∠D

In a kite, the angle between unequal sides is equal.

Let's prove the same.

Draw a line from A to C and we will get two triangles with common base AC.

In ∆ABC and ∆ADC we have,

AB = AD,

BC = CD

AC is common to both

∆ABC **≅ **∆ADC (Using SSS congruence)

Hence corresponding parts of congruent triangles are equal.

Therefore ∠B = ∠D (By CPCT)

However, the quadrilateral ABCD is not a parallelogram as the measures of the remaining pair of opposite angles, ∠A and ∠C are not equal since they form angles between equal sides.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 3

**Video Solution:**

## Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 4

**Summary:**

A rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is drawn. The figure is a Kite.

**☛ Related Questions:**

- The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.
- Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
- The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
- The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

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