Question

ABCD is a parallelogram the bisectors of consecutive angles A and B intersect at O show that angle AOB=90°​

Answer 1

Answer:

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Answer 2

Use Properties of Triangles

Step-by-step explanation:

Given, ABCD is a Parallelogram

where AD is parallel to BC and AB is the transversal.

Now, As ΔBAD & ΔCBA = 180 (Angles on the same side of transversal)

As per the question,  

$\frac{1}{2}\angle{BAD} +  \frac{1}{2}\angle{CBA} = \frac{1}{2}(180)$

⇒ $\angle 1 +\angle 2 = 90$

So, In ΔAOB,

By Angle Sum Property of Triangles,  

$\angle 1 + \angle 2 + \angle AOB = 180$

⇒ $\angle AOB = 180 - \angle 1 - \angle 2$

So, $\angle AOB = 90$

Hence, Bisectors of any two consecutive angles of a parallelogram intersect at Right Angles