Construction of Angle and Angle Bisector
Construction of Angle and Angle Bisector
Bisecting an angle means drawing a ray in the interior of the angle, with its initial point at the vertex of the angle such that it divides the angle into two equal parts
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| In order to draw a ray AX bisecting a given angle |
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| STEP I With centre A and any convenient radius draw an are cutting AB and AC at P and Q respectively. |  |
| STEP II With centre P and radius more than half of PQ draw an arc. |  |
| STEP III With centre Q and the same radius,as in step II, draw another arc intersecting the arc in step II at R. |  |
| STEP IV Join AR and produce it to any point X. The ray AX is the required bisector of |
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Verification: Measure and
You would find that
Justification: Now let us see how this method gives us the required angle bisector.
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Join PR and QR. In AP = AQ [ PR = QR [ AR = AR [common] So, Hence, AR is the bisector of |
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ILLUSTRATION: Using a protractor, draw an angle of mesure . With this angle as given, draw an angle of measure
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SOLUTION We follow the following steps to draw an angle of from an angle of .
Steps of Construction
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STEP I Draw a ray OA as shown in fig. STEP II With the help of a protractor contruct an angle AOB of measure |
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| STEP III WIth centre O and a convenient radius draw an arc cutting sides OA and OB at P and Q respectively. |  |
| STEP IV With centre P and radius more than half of PQ, draw an arc. |  |
| STEP V With centre Q and the same radius, as in the previous step, draw another arc intersecting the arc drawn in the previous step at R. |  |
| STEP VI Join OR and produce it to form ray OX. |  |
| The angle |
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If we bisect an angle of a rectangle , we get 2 angles each of ________ | |||
| Right Option : A | |||
| View Explanation | |||
Angle bisector of given angle can be constructed accurately using ________________. | |||
| Right Option : A | |||
| View Explanation | |||
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