Sujeet Kumar

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.Find the values of x and y using the information shown in the given figure. Find the measures of ∠ABD and ∠ACD. Solution:i. ∠ACB = 50° [Given]In ∆ABC, seg AC ≅ seg AB [Given]∴ ∠ABC ≅ ∠ACB [Isosceles triangle theorem]∴ x = 50° ii. ∠DBC = 60° [Given]In ABDC, seg BD ≅ seg DC … Read more

Question 1.In each of the examples given below, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same signs. Observe the figures and state the test by which the triangles in each pair are congruent. By SSS test∆ABC ≅ ∆PQR By SAS test∆ XYZ ≅ ∆LMN By … Read more

Question 1.In the adjoining figure, ∠ACD is an exterior angle of ∆ABC. ∠B = 40°, ∠A = 70°. Find the measure of ∠ACD. Solution:∠A = 70° , ∠B = 40° [Given]∠ACD is an exterior angle of ∆ABC. [Given]∴ ∠ACD = ∠A + ∠B= 70° + 40°∴ ∠ACD = 110° Question 2.In ∆PQR, ∠P = 70°, … Read more

Question 1.Select the correct alternative and fill in the blanks in the following statements. i. If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ____.(A) 0°(B) 90°(C) 180°(D) 360°Answer:(C) 180° ii. The number of angles formed by a transversal of two lines is … Read more

Question 1.In the given figure, y = 108° and x = 71°. Are the lines m and n parallel? Justify? Solution:y = 108°, x = 71° …[Given]x + y = 71° + 108°= 179°∴ x + y = 180°∴ The angles x andy are not supplementary.∴ The angles do not satisfy the interior angles test … Read more

Question :In the given figure, line RP || line MS and line DK is their transversal. ∠DHP = 85°. Find the measures of following angles. i. ∠RHDii. ∠PHGiii. ∠HGSiv. ∠MGKSolution:i. ∠DHP = 85° …..(i)∠DHP + ∠RHD = 180° [Angles in a linear pair]85° + ∠RHD = 180°∴ ∠RHD = 180°- 85°∴ ∠RHD = 95° …..(ii) … Read more

Question 1.Select the correct alternative answer for the questions given below. i. How many midpoints does a segment have ?(A) only one(B) two(C) three(D) manyAnswer:(A) only one ii. How many points are there in the intersection of two distinct lines ?(A) infinite(B) two(C) one(D) not a singleAnswer:(C) one iii. How many lines are determined by … Read more

Question 1.Write the following statements in ‘if-then’ form.i. The opposite angles of a parallelogram are congruent.ii. The diagonals of a rectangle are congruent.iii. In an isosceles triangle, the segment joining the vertex and the midpoint of the base is perpendicular to the base.Answer:i. If a quadrilateral is a parallelogram, then its opposite angles are congruent.ii. … Read more

Question 1.The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not. i. seg DE and seg ABii. seg BC and seg ADiii. seg BE and seg ADSolution:i. Co-ordinate of the point E is 9.Co-ordinate of the point D is … Read more