Question

Prove that the bisectors of the angles of a linear pair are at a right angle​

Answer 1

Answer:

we know that linear pair of angle is180 degrees.

angle bisector means it divides the angle into two equal angles.

so,180/2=90 degrees.

that means each angle should be 90 degree. And we  know that 90 degree is known as

right angle .hence proved.

                                                          or

Angles ACD and DCB are a linear pair. Sum of these angles = 180 deg

ACD + DCB = 180 deg

CE is bisector of angle ACD.

CF is bisector of angle DCB.

To prove that angle ECF = 90 deg.

ECF = ECD + DCF = 1/2 ACD + 1/2 DCB

        = 1/2 { angle ACD + angle DCB ] = 1/2 180 deg = 90 deg

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Answer 2

Answer:

Step-by-step explanation:

Angles ACD and DCB are a linear pair. Sum of these angles = 180 deg

ACD + DCB = 180 deg

CE is bisector of angle ACD.

CF is bisector of angle DCB.

To prove that angle ECF = 90 deg.

ECF = ECD + DCF = 1/2 ACD + 1/2 DCB

= 1/2 { angle ACD + angle DCB ] = 1/2 180 deg = 90 deg