Sujeet Kumar

Question 1.In □IJKL, side IJ || side KL, ∠I = 108° and ∠K = 53°, then find the measures of ∠J and ∠L.Solution: i. ∠I = 108° [Given]side IJ || side KL and side IL is their transveral. [Given]∴ ∠I + ∠L = 180° [Interior angles]∴ 108° + ∠L = 180°∴ ∠L = 180° – … Read more

Question 1.Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm, then find BO and if ∠CAD = 35°, then find ∠ACB.Solution: i. AC = 8 cm …(i) [Given]□ABCD is a rectangle [Given]∴ BD = AC [Diagonals of a rectangle are congruent]∴ BD = 8 cm [From (i)]∴ BO = 4 … Read more

Question 1.In the adjoining figure, □ABCD is a parallelogram, P and Q are midpoints of sides AB and DC respectively, then prove □APCQ is a parallelogram. Given: □ABCD is a parallelogram. P and Q are the midpoints of sides AB and DC respectively.To prove: □APCQ is a parallelogram.Solution:∴ AP = QC ….(iii) [From (i) and … Read more

Question 1.Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ∠ = 135°, then measure of ∠XWZ and ∠YZW? If l(OY) = 5 cm, then l(WY) = ?Solution: i. ∠XYZ = 135°□WXYZ is a parallelogram.∠XWZ = ∠XYZ∴ ∠XWZ = 135° …..(i) ii. ∠YZW + ∠XYZ = 180° [Adjacent angles of a parallelogram … Read more

Question 1.Construct ∆XYZ, such that XY + XZ = 10.3 cm, YZ = 4.9 cm, ∠XYZ = 45°.Solution: As shown in the rough figure draw segYZ = 4.9cmDraw a ray YT making an angle of 45° with YZTake a point W on ray YT, such that YW= 10.3 cmNow,YX + XW = YW [Y-X-W]∴ YX … Read more

Question 1.Construct ∆PQR, in which ∠Q = 70°, ∠R = 80° and PQ + QR + PR = 9.5 cm.Solution: i. As shown in the figure, take point T and S on line QR, such thatQT = PQ and RS = PR ….(i)QT + QR + RS = TS [T-Q-R, Q-R-S]∴ PQ + QR + … Read more

Question 1.Construct ∆XYZ, such that YZ = 7.4 cm, ∠XYZ = 45° and XY – XZ = 2.7 cm.Solution: Here, XY – XZ = 2.7 cm∴ XY > XZAs shown in the rough figure draw seg YZ = 7.4 cmDraw a ray YP making an angle of 45° with YZTake a point W on ray … Read more

Question 1.Construct APQR, in which QR = 4.2 cm, m∠Q = 40° and PQ + PR = 8.5 cm.Solution: As shown in the rough figure draw seg QR = 4.2 cmDraw a ray QT making an angle of 40° with QRTake a point S on ray QT, such that QS = 8.5 cmNow, QP + … Read more

Question 1.In the adjoining figure, point A is on the bisector of ∠XYZ. If AX = 2 cm, then find AZ. Solution:AX = 2 cm [Given]Point A lies on the bisector of ∠XYZ. [Given]Point A is equidistant from the sides of ∠XYZ. [Every point on the bisector of an angle is equidistant from the sides … Read more

Question 1.Choose the correct alternative answer for the following questions. i. If two sides of a triangle are 5 cm and 1.5 cm, the length of its third side cannot be ____.(A) 3.7 cm(B) 4.1 cm(C) 3.8 cm(D) 3.4 cmAnswer:Sum of the lengths of two sides of a triangle > length of the third sideHere, … Read more