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Question
Draw ∠ABC = 120°. Bisect the angle using a ruler and compasses only. Measure each angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not.
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Solution
Steps of construction :
Step 1: Draw a line segment BC.
Step2: With centre B and some suitable radius, draw an arc meeting BC at P. Again With centre P and with the same radius, cut arcs PQ and QR.
Step 3: Join BR and produce it to A.
Then ∠ABC = 120°
Step 4:With centres P and R, draw two arcs intersecting each other at S.
Step5: Join BS and produce it to D. BD is the bisector of ∠ABC.
On measuring each angle, it is 60° each. Yes, both angles are equal in measure.
Step 1: Draw a line segment BC.
Step2: With centre B and some suitable radius, draw an arc meeting BC at P. Again With centre P and with the same radius, cut arcs PQ and QR.
Step 3: Join BR and produce it to A.
Then ∠ABC = 120°
Step 4:With centres P and R, draw two arcs intersecting each other at S.
Step5: Join BS and produce it to D. BD is the bisector of ∠ABC.
On measuring each angle, it is 60° each. Yes, both angles are equal in measure.
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