2. Plot the points (x, y) given in the following table on the plane, choosing suitable unitsof distance on the axes.
1. In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0),(1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.
1.(v) Find the remainder when is divided by
6. In Fig. 6.44, the side QR of PQR is produced to a point S. If the bisectors of PQR and PRS meet at point T, then prove that QTR = QPR.
5. In Fig. 6.43, if PQ PS, PQ SR, SQR = 28° and QRT = 65°, then find the values of x and y.
4. In Fig. 6.42, if lines PQ and RS intersect at point T, such that PRT = 40°, RPT = 95° and TSQ = 75°, find SQT.
3. In Fig. 6.41, if AB DE, BAC = 35° and CDE = 53°, find DCE.
2. In Fig. 6.40, X = 62°, XYZ = 54°. If YO and ZO are the bisectors of XYZ and XZY respectively of XYZ, find OZY and YOZ.
1. In Fig. 6.39, sides QP and RQ of PQR are produced to points S and T respectively. If SPR = 135° and PQT = 110°, find PRQ.
6. In Fig. 6.33, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB CD.
5. In Fig. 6.32, if AB CD, APQ = 50° and PRD = 127°, find x and y.
4. In Fig. 6.31, if PQ ST, PQR = 110° and RST = 130°, find QRS.
[Hint : Draw a line parallel to ST through point R.]
3. In Fig. 6.30, if AB CD, EF CD and GED = 126°, find AGE, GEF and FGE.
2. In Fig. 6.29, if AB CD, CD EF and y : z = 3 : 7, find x.
1. In Fig. 6.28, find the values of x and y and then show that AB CD.
6. It is given that XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ZYP, find XYQ and reflex QYP.
5. In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that
4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
3. In Fig. 6.15, PQR = PRQ, then prove that PQS = PRT.
2. In Fig. 6.14, lines XY and MN intersect at O. If and a : b = 2 : 3, find c.