Question

3. Can a quadrilateral ABCD be a parallelogram if () ZD+ ZB = 180°? (ii) AB = DC = 8 cm. AD = 4 cm and BC = 4.4 cm? (ii) ZA = 70° and ZC = 65°?
answer ​

Answer 1

Answer:

HI GUYS,

YOUR ANSWER IS:-

(i) Using the angle sum property of a quadrilateral,

∠A + ∠B + ∠D + ∠C = 360°

∠A + ∠C + 180° = 360° (Since its given that ∠D + ∠B = 180°)

∠A + ∠C = 360° -180°

∠A + ∠C = 180° (Opposite angles should also be of same measures.)

For ∠D + ∠B = 180°, is a parallelogram.

AD = 4cm and BC = 4.4 cm.

So, ∠A = 70° and ∠C = 65°

THANKS A LOT FOR YOUR SUPPORT

Answer 2

Answer:

Step-by-step explanation:

Answer:

A quadrilateral is a parallelogram if

i)Its opposite sides are equal

ii) its opposite angles are equal

iii) diagonals bisect each other

iv) a pair of opposite sides is equal and parallel.

v) The sum of the adjacent angles should be 180∘

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Solution:

i)

if ∠D + ∠B = 180°, a quadrilateral ABCD may or may not be a parallelogram

but it should also fulfilled some conditions which are as:

The sum of the adjacent angles should be 180∘

 

Opposite angles must be of  equal length.

 

(ii) No, opposite sides should be of same length. Here, opposite sides are of different lengths. AD ≠ BC

 

(iii) No, opposite angles should be of same measures. Here opposite angles are of different measures. ∠A ≠ ∠C.

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