Grade 7 Triangle and its properties

Transcription

1 ID : ww-7-triangle-and-its-properties [1] Grade 7 Triangle and its properties For more such worksheets visit Answer t he quest ions (1) Find missing angle (2) If AB and CD are parallel, f ind the value of x+y. (3) Find sum of f ollowing angles, a + b + c + d + e + f =?

2 (4) Find missing angle ID : ww-7-triangle-and-its-properties [2] (5) If a triangle ABC is drawn so that sides AB and AC are equal and C is 15, then what is the value of angle A? (6) Find sum of f ollowing angles, pqr + qrs + rst + stu + tup+ upq =? Choose correct answer(s) f rom given choice (7) If angle A is a right angle, f ind perimeter of the triangle (All dimensions are in meters). a. 436 meters b. 431 meters c. 432 meters d. 435 meters (8) The hypotenuse of a right angle triangle is 90 meters long. If one of the remaining side is 54 meters long, what is the length of another side? a. 70 meters b. 75 meters c. 72 meters d. 76 meters

3 (9) If line AC and DE are parallel to each other, f ind value of angle x? ID : ww-7-triangle-and-its-properties [3] a. 65 b. 55 c. 60 d. 115 (10) If distance between B and D is 90 cm, f ind the distance between A and C. a. 71 cm b. 72 cm c. 80 cm d. 74 cm Fill in the blanks (11) If angles in a triangle are p - 10, p + 20 and p + 50, value of p =? (12) A triangle has three angles, which we call the f irst, second and third angle here. The second angle is twice the f irst angle. The third angle is 138. The f irst angle is. (13) Value of missing angle =

4 ID : ww-7-triangle-and-its-properties [4] Check True/False (14) Side lengths of 29 cm, 21 cm and 20 cm make a right angle triangle. True False (15) In triangle ΔABC and ΔPQR, If A = Q, AC = QP and BA = RQ, T riangles are congruent. True False 2016 Edugain ( All Rights Reserved Many more such worksheets can be generated at

5 Answers ID : ww-7-triangle-and-its-properties [5] (1) 31 Lets assume the missing angle is x. The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. If you look at the given triangle caref ully, you will notice that the exterior angle of the given triangle = x = x = x x = x = 31 Step 4 Theref ore the missing angle is 31. (2) 105 According to question AB and CD are parallel, theref ore x = 45 [Alternate interior angles] y = 60 [Alternate interior angles] Now the value of x+y = = 105

6 (3) 360 ID : ww-7-triangle-and-its-properties [6] If you look at the given f igure caref ully, you will notice that it is a combination of triangle ace and triangle bdf. Since the sum of all three angles of a triangle is 180. Theref ore a + c + e = 180, b + d + f = 180 Now the sum of the angles a + b + c + d + e + f = = 360 (4) 48 In the triangle ABC, C = 88...[Vertically opposite angles] Now, in triangle ABC, B = [The sum of all three angles of a triangle is equals to 180 ] B = 48 T he missing angle = B = 48...[Vertically opposite angles] Step 4 Theref ore, the value of missing angle is 48.

7 (5) 150 ID : ww-7-triangle-and-its-properties [7] Following f igure shows the triangle ABC, An isosceles triangle is a triangle with (at least) two equal sides. According to the question, the side AB is equals to the side AC, the triangle ABC is an isosceles triangle. In an isosceles triangle the angles opposite to the equal sides, are equal. Hence B equals C. Since, angle C = 15, theref ore, B = 15. The sum of all the angles of a triangle is equals to 180. Theref ore, A + B + C = 180 or A = 180 or A + 30 = 180 or A = or A = 150 Step 4 Thus, the value of the A is 150. (6) 720 If you look at the f igure caref ully, you will notice that it is a combination of 4 triangles and the sum of angles pqr + qrs + rst + stu + tup+ upq is equal to the sum of the angles of all 4 triangles. The sum of all three angles of a triangle is 180, theref ore the sum of all the angles of 4 triangles is = = 720, and hence the sum of the angles pqr + qrs + rst + stu + tup+ upq is 720.

8 (7) c. 432 meters ID : ww-7-triangle-and-its-properties [8] According to question in triangle ΔABC angle A is a right angle, theref ore the triangle ΔABC is a right angle triangle. Lets assume length of BC is x meters. In ΔABC BC 2 = AB 2 + AC = x 2 By solving it, x = 144. The length of BC is 144 meters. Now the perimeter of right angle triangle ΔABC = AB + AC + BC = = 432 meters

9 (8) c. 72 meters ID : ww-7-triangle-and-its-properties [9] Lets assume the length of another side of a right angle triangle is x meters long. According to question the hypotenuse of a right angle triangle is 90 meters long and one of the remaining side is 54 meters long as shown in the f ollowing right angle triangle. Since ΔABC is a right angle triangle, theref ore in ΔABC AB 2 + BC 2 = AC 2 x = 90 2 x = 8100 x 2 = x 2 = 5184 x 2 = 72 2 x = 72 Step 4 Now the length of another side is 72 meters.

10 (9) a. 65 ID : ww-7-triangle-and-its-properties [10] If you look at the question caref ully, you will notice that line AC and DE are parallel to each other and BAC = 55 BDE = BAC [Corresponding angles] BDE = 55 The sum of all the three angles of a triangles is 180. In triangle BDE BDE + BED + DBE = BED + 60 = 180 BED = 180 BED = BED = 65 x = 65 Theref ore the value of angle x is 65.

11 (10) b. 72 cm ID : ww-7-triangle-and-its-properties [11] According to question the distance between B and D is 90 cm and you have to f ind out the distance between A and C. Lets assume the distance between A and C is x cm. Lets connect the point B to point D as shown in the f ollowing f igure. If you look at the f igure caref ully, you will notice that ΔBED is a right angle triangle and the distance between A and C is equal to the distance between D and E, BE = AB - CD = = 54 cm In ΔBED BD 2 = DE 2 + BE = x By solving it, x = 72. Now the distance between A and C is 72 cm.

12 (11) 40 ID : ww-7-triangle-and-its-properties [12] According to question the angles in a triangle are p - 10, p + 20 and p The sum of all three angles of a triangle must be 180. Theref ore (p - 10) + (p + 20) + (p + 50) = 180 p p p + 50 = 180 3p + 60 = 180 3p = p = p = 40 Now the value of p is 40. (12) 14 Let the measure of the f irst angle be a. We have been told that the second angle is twice the f irst angle. This means that the measure of the second angle is 2a. We have also been told that the measure of the third angle is 138. Thus: First angle = a Second angle = 2a, and Third angle = 138 Step 4 We know that the sum of all interior angles of a triangle is 180. Thus we can write: a + 2a = 180 3a = a = 42 3 a = 14 Step 5 Hence, the value of the f irst angle is 14.

13 (13) 80 ID : ww-7-triangle-and-its-properties [13] If you look at the given triangle caref ully, you will notice that the two angles of the triangle are given. Lets assume the third angle of the triangle is x. The sum of all three angles of a triangle is equal to 180. In given triangle x = x = 180 x = x = 80 Now the missing angle = angle x [Opposite angles] and hence the value of missing angle is 80. (14) True The square of the largest side of a right angle triangle is equal to the sum of square of the other two sides. The square of the largest side f rom side lengths 21 cm, 20 cm and 29 cm can be written as: 29 2 = = = 841 Now you will notice that the square of the largest side is equal to the sum of square of the other two sides and hence the statement "Side lengths of 21 cm, 20 cm and 29 cm make a right angle triangle" is True.

14 (15) True ID : ww-7-triangle-and-its-properties [14] T wo triangles are congruent if their corresponding sides or angles are equal, as shown below. According to question in triangle ΔABC and ΔPQR, A = Q, AC = QP and BA = RQ By SAS(side angle side) Congruence Rul, triangle ΔABC is congruent to ΔPQR and hence the correct answer is True.