Page 146 - classs 6 a_Neat

EXAMPLE:3 An angle LAOB is given. Draw a ray ox, bisecting LAOB. TO DRAW A LINE PAR ALLEL TO A GIVEN LINE THROUGH A POINT OUTSIDE IT
Steps of construction
Let AOB be given. EXAMPLE: 6 A line XY is given and Pis a point outside it. Draw a line through P parallel to XY.
1. With O as centre and any convenient radius, draw an arc. Steps of construction
cutting OA and OB at P and Q respectively. Let XY be the given line and P be a given point outside it. R P
2. With centre P and radius more than - (PQ), draw an arc. 1.Take any point Q on XY.
3. With centre Q and the same radius as before, draw another 2.Join QP.
arc, cutting the previously drawn arc at a point R. 3.Draw RPQ such that RPQ = PQY
4. Join OR and produce it to any point X. as shown in the figure. X Q Y
Then, ray OX bisects AOB. 4.Extend RP on both sides.
Verification Measure AOX and BOX. Then, the line RP passes through the point P and RP || XY.
You would find that AOX = BOX.

TO DRAW A LINE PERPENDICULAR TO A GIVEN LINE FROM A POINT ON IT
EXAMPLE:4 A line XY is given and Pis a point on it. Draw a line through P perpendicular to XY.
Steps of construction
Let XY be the given line and P be a point on it.
1. With centre P and any radius, draw a semicircle to intersect XY at A and B.
2. With centre A and any radius more than PA, draw an arc.
3. With centre B and the same radius, draw another arc,
cutting the previously drawn arc at Q.
4. JoinPQ.
Then, QP 1- XY.
Verification Measure QPX and QPY.
You would find that QPX = QPY = 90°.

TO DRAW A LINE PERPENDICULAR TO A GIVEN LINE FROM A POINT OUTSIDE IT
EXAMPLE:5 A line XY is given and P ts a point outside it. Draw a line through P perpendicular
to XY.
Steps of construction
Let XY be the given line and P be a point outside it.
1. With P as centre and a convenient radius, draw an arc
intersecting XY at A and B.
2.With A as centre and a radius greater than - (AB), draw
an arc.
3.With Bas centre and the same radius, draw another arc,
cutting the previously drawn arc at Q.
4.Join PQ, meetingXY at L.
Then, PL is the required perpendicular on XY.

Verification Measure LPLX and LPLY.
You would find that LPLX = LPLY = 90° .