ID : ae-7-triangle-and-its-properties [1] Grade 7 Triangle and its properties For more such worksheets visit www.edugain.com Answer t he quest ions (1) In triangle In ΔABC, D is a point on the side BC such that AB = AD = DC. If BAD = 40, f ind the angle BAC. (2) If angle BDC and ACB are right angles, f ind the value of angle DCB. (3) If line AC and DE are parallel to each other, f ind value of angle x? Choose correct answer(s) f rom given choice (4) Angle R is a right angle, and PS and QS are bisector of angles P and Q respectively. Find the angle PSQ. a. 140 b. 135 c. 145 d. 125 (5) Which of f ollowing is f alse f or a triangle? a. One angle is obtuse angle b. Two angles are acute angles c. Each angle is less than 60 d. Each angle is equal to 60
(6) In a triangle PQR, if R > P, which of f ollowing is true. a. RQ < RP b. RQ > RP ID : ae-7-triangle-and-its-properties [2] c. PQ > RQ d. PQ > RP (7) Which is the largest angle of this triangle? a. A b. C c. B d. Can not be determined Fill in the blanks (8) If angle A is a right angle, perimeter of the triangle is meters (All dimensions are in meters). (9) The hypotenuse of a right angle triangle is 74 cm long. If one of the remaining side is 70 cm long, the length of another side is cm. (10) A triangle that has two sides and only two sides as equal is called an triangle (11) Value of missing angle = (12) Ameerah is walking in south direction. Af ter walking f or 45 meters, she takes a right turn, and walks f or another 108 meters. She is at a distance of meters f rom starting point.
ID : ae-7-triangle-and-its-properties [3] (13) Value of missing angle = (14) If a triangle ABC is drawn so that sides AB and AC are equal and C is 60, then the value of angle A is. Check True/False (15) Side lengths of 80 m, 120 m and 84 m make a right angle triangle. True False 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ae-7-triangle-and-its-properties [4] (1) 75 (2) 50 We know that the sum of all interior angles of a triangle is 180. Theref ore, f or triangle ΔABC, CBD + BCA + CAD = 180 CBD + 90 + 50 = 180 CBD = 180 - (50 + 90 ) CBD = 40 Similarly, f or the triangle ΔCDB, CBD + DCB + CDB = 180 40 + DCB + 90 = 180 DCB = 180 - (40 + 90 ) DCB = 50
(3) 70 ID : ae-7-triangle-and-its-properties [5] 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 = 180 55 + BED + 55 = 180 BED + 110 = 180 BED = 180-110 BED = 70 x = 70 Theref ore the value of angle x is 70.
(4) b. 135 ID : ae-7-triangle-and-its-properties [6] We know sum of internal angles of triangle is 180 Theref ore f or triangle Δ RQP RQP + QPR + PRQ = 180 RQP + QPR + 90 = 180 RQP + QPR = 180-90 RQP + QPR = 90 On dividing above equation by 2 RQP/2 + QPR/2 = 90 /2 SQP + QPS = 45 Step 4 Sum of internal angles of triangle Δ SQP SQP + QPS + PSQ = 180 45 + PSQ = 180 PSQ = 180-45 PSQ = 135 (5) c. Each angle is less than 60 The sum of all three angles of a triangle must be 180. Now if you look at the all of the options caref ully, you will notice that the statement "Each angle is less than 60 ", can't satisf y the condition of a triangle and hence the statement "Each angle is less than 60 " is f alse.
(6) c. PQ > RQ ID : ae-7-triangle-and-its-properties [7] In a triangle the shortest side is always opposite to the smallest interior angle and the longest side is always opposite to the largest interior angle as shown below. According to question, in triangle RPQ the R > P. Theref ore PQ > RQ and hence the correct answer is PQ > RQ. (7) c. B The largest side of a triangle is always opposite to the largest interior angle or you can say that the largest angle is always opposite to the largest side of a triangle. If you look at the triangle caref ully, you will notice that angle B is opposite to the largest side of the triangle. Now you can say that the largest angle of this triangle is B.
(8) 260 ID : ae-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 AC is x meters. In ΔABC BC 2 = AB 2 + AC 2 x 2 = 91 2 + 60 2 By solving it, x = 109. The length of AC is 109 meters. Now the perimeter of right angle triangle ΔABC = AB + AC + BC = 91 + 60 + 109 = 260 meters
(9) 24 ID : ae-7-triangle-and-its-properties [9] Lets assume the length of another side of a right angle triangle is x cm long. According to question the hypotenuse of a right angle triangle is 74 cm long and one of the remaining side is 70 cm 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 2 + 70 2 = 74 2 x 2 + 4900 = 5476 x 2 = 5476-4900 x 2 = 576 x 2 = 24 2 x = 24 Step 4 Now the length of another side is 24 cm.
(10) isosceles ID : ae-7-triangle-and-its-properties [10] A triangle having two sides of equal length is called an isosceles triangle. Let's understand through the f ollowing illustration: In the f igure above, ABC is a triangle in which AB BC = CA. Step 4 Thus we have learnt that a triangle that has two sides and only two sides as equal is called an Isosceles T riangle.
(11) 79 ID : ae-7-triangle-and-its-properties [11] In the triangle ABC, A = 52...[Vertically opposite angles] Now, in triangle ABC, C + 52 + 49 = 180...[The sum of all three angles of a triangle is equals to 180 ] C = 79 T he missing angle = C = 79...[Vertically opposite angles] Step 4 Theref ore, the value of missing angle is 79.
(12) 117 ID : ae-7-triangle-and-its-properties [12] Lets assume Ameerah is walking in south direction f rom the point A. Af ter walking f or 45 meters, she takes a right turn, and walks f or another 108 meters, and she is x meters f rom starting point as shown in the f ollowing f igure. If you look at the f igure caref ully, you will notice that the given f igure is a right angled triangle. Theref ore you can say that x 2 = 45 2 + 108 2 x 2 = 2025 + 11664 x 2 = 13689 x 2 = 117 2 x = 117 Now Ameerah is 117 meters f ar f rom the starting point.
(13) 42 ID : ae-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 51 + 87 + x = 180 138 + x = 180 x = 180-138 x = 42 Now the missing angle = angle x [Opposite angles] and hence the value of missing angle is 42.
(14) 60 ID : ae-7-triangle-and-its-properties [14] 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 = 60, theref ore, B = 60. The sum of all the angles of a triangle is equals to 180. Theref ore, A + B + C = 180 or A + 60 + 60 = 180 or A + 120 = 180 or A = 180-120 or A = 60 Step 4 Thus, the value of the A is 60. (15) False 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 84 m, 80 m and 120 m can be written as: 120 2 = 84 2 + 80 2 14400 = 7056 + 6400 14400 = 13456 Now you will notice that the square of the largest side is not equal to the sum of square of the other two sides and hence the statement "Side lengths of 84 m, 80 m and 120 m make a right angle triangle" is False.