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Constructing a Parallelogram When Its Two Diagonals and One Included Angle Are Given

Construct a p...

Question

Construct a parallelogram, ABCD with AB = 3.5 cm, BC = 4.5 cm and diagonal BD = 5.5 cm. [2 MARKS]

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Solution

Concept and steps : 1 Mark
Construction : 1 Mark

Concept :
A diagonal divides the parallelogarm into two triangles.

Steps of construction :
1. Construct a $Δ B C D$ with SSS method.
2. Construct a $Δ B C D$ with BD as base using SSS method.

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Similar questions

Construct a quadrilateral, ABCD with AB = 3.5 cm, BC = 3.0 cm, AD = 3.8 cm, diagonal AC = 5.0 cm and diagonal BD = 4.5 cm.
[2 MARKS]

Construct a parallelogram, ABCD with side BC = 4.5 cm, diagonal AC = 5.6 cm and diagonal BD = 5.0 cm. [4 MARKS]

Construct quadrilateral ABCD given BC = 4.5 cm, AD = 5.5 cm, CD = 5 cm, diagonal AC = 5.5 cm and diagonal BD = 7 cm.

Construct the following quadrilaterals.

(i) Quadrilateral $A B C D$

$A B = 4.5 c m$

$B C = 5.5 c m$

$C D = 4 c m$

$A D = 6 c m$

$A C = 7 c m$

J U M P

J U = 3.5 c m

U M = 4 c m

M P = 5 c m

P J = 4.5 c m

P U = 6.5 c m

M O R E

O R = 6 c m

R E = 4.5 c m

E O = 7.5 c m

B E S T

B E = 4.5 c m

E T = 6 c m

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