Question

In your notebook, draw a right angle and then draw a bisector of the right angle. Label all parts. What are some properties of the angles formed by the bisector? Use complete sentences for full credit.

Answer 1

Solution:   Construct a right angle triangle ABC right angled at B.

To construct angle bisector of right angle ,we need to draw arcs from A and C on both the sides with the use of protector.

then join both the intersections of arcs to make the bisector PQ which intersect AC at D.

Now as it is bisecting the right angle B ,therefore as ∠B = 90°

⇒ ∠ABD+∠DBC= 90°

⇒∠ABD+∠ABD= 90°

[ As angle bisector bisects the angle into two equal halves,∴∠A =∠DBC]

⇒2∠ABD= 90°

⇒∠ABD=45° =∠DBC

Answer 2

Let's consider this right triangle described in the picture. ∠ABD = ∠CBD, since BD is a bisector.
Angles ∠ADB and ∠BDC are neighbor angles and their sum is equal to 180°.
∠BDC is an exterior angle and ∠BDC=∠ABD+∠ADB.
Similarly, ∠ADB is an exterior angle and ∠ADB=∠CBD+∠BCD