Question

class 9(solve20part)

Answer 1

Then, its proved that the bisector two consecutive angles of a parallelogram are perpendicular to each other.

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Answer 2

Question 20
Solution:

Given: A parallelogram ABCD where consecutive angles A and B are bisected by lines produced from A and B meeting at D

To prove: AD and BD are perpendicular to each other i.e, angle ADB = 90°
Proof:
Since angle A and angle B are a pair of consecutive angles of parallelogram ABCD,
angle A + angle B = 180°
=> 1/2 × (angle A + angle B) = 1/2 × 180
[Multiplying both sides by 1/2]
=> 1/2×angle A + 1/2×angle B = 90
=> angle DAB + angle DBA = 90 ---- (1)
[because AD bisects angle A and BD bisects angle B]

Now, in triangle ADB
by angle sum property, we have,
angle DAB + angle DBA + angle ADB = 180°
=> 90° + angle ADB = 180° [from (1)]
=> angle ADB = 180° - 90°
=> angle ADB = 90 °
Hence proved