Construct a quadrilateral ABCD in which AB = AD = 5cm, BC = CD = 7cm and BD = 6cm. What type of quadrilateral is this
Solution:
Given, ABCD is a quadrilateral.
AB = AD = 5 cm
BC = CD = 7 cm
BD = 6 cm
We have to find the type of quadrilateral.
(i) Draw a line segment BD = 6 cm
(ii) Taking B and D as centres and 5 cm radius, draw arcs to intersect at the point A.
(iii) Join AB and AD
(iv) Taking B and D as centres and 7 cm radius, draw arcs in the opposite side of A to intersect at the point C.
(v) Join BC and DC
ABCD is the required quadrilateral.
A Kite is a quadrilateral in which four sides can be grouped into two pairs of equal-length sides that are adjacent to each other and the diagonals intersect each other at right angles.
AB = AD and BC = BD implies that two pairs of equal-length sides are adjacent to each other.
Therefore, ABCD is a kite.
✦ Try This: Construct a quadrilateral PQRS in which PQ = QR = RS = PS = 6cm. What type of quadrilateral is this?
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 26
Construct a quadrilateral ABCD in which AB = AD = 5cm, BC = CD = 7cm and BD = 6cm. What type of quadrilateral is this
Summary:
Construct a quadrilateral ABCD in which AB = AD = 5cm, BC = CD = 7cm and BD = 6cm. ABCD is a kite.
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