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 we follow the following steps. | |
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 . |
Verification: Measure and You would find that
Justification: Now let us see how this method gives us the required angle bisector.
Join PR and QR. In APR and AQR, we have AP = AQ [ AP and AQ are radii of the same arc] PR = QR [ PR and QR are arcs of equal radii.] AR = AR [common] So, APR AQR [by SSS congruence criterion ] [C.P.C.T.] Hence, AR is the bisector of |
ILLUSTRATION: Using a protractor, draw an angle of mesure . With this angle as given, draw an angle of measure .
SOLUTION We follow the following steps to draw an angle of from an angle of .
Steps of Construction
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 so obtained the required angle of measure |
Angle bisector of given angle can be constructed accurately using ________________. | |||
Right Option : A | |||
View Explanation |
If we bisect an angle of a rectangle , we get 2 angles each of ________ | |||
Right Option : A | |||
View Explanation |
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