costruct an angular bisector for an angle 90 degree and justify your answer
Answers
Answer:
tep 1 : Put the sharp end of your compasses at point B and make one arc on the line BC (point S) and another arc on line AB (point T
Step 2 : Put the sharp end of the compasses at S and make an arc within the lines AB and BC. Do the same at T and make sure that the second arc intersects the first arc.
construct angle bisector
Step 3 : Draw a line from point B to the points of intersection of the 2 arcs. This line bisects ∠ABC.
construct angle bisector
The steps to construct an angle bisector can be summarized as follows:
1. From the vertex, draw an arc across both rays of the angle.
2. From each arc intersection draw another pair of arcs that intersect each other.
3. Draw a line from the vertex to the intersection point to form the angle bisector.
How to draw an angle bisector using a compass and a straight edge?
1. Place compass point on the vertex, and draw an arc across each ray.
2. Place the compass on each arc intersection and draw a further pair of arcs which intersect each other.
3. Use a straight edge to connect the intersection point to the vertex.
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How to bisect a given angle using only a compass and straightedge?
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Use angle bisector to construct angles
We can use the angle bisector to construct some other angles from existing angles.
Example :
A 30˚ angle can be obtained by bisecting a 60˚ angle.
A 15˚ angle can be obtained by bisecting a 30˚ angle.
A 45˚ angle can be obtained by bisecting a 90˚ angle.
A 22.5˚ angle can be obtained by bisecting a 45˚ angle.
Example:
The figure shows a point A on a straight line. Construct an angle of 45˚ at point A.
Solution:
Construct a 90˚ angle, and then construct an angle bisector to obtain a 45˚ angle.
Step-by-step explanation: