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.
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