Triangle and its Properties

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Lionel Fowler
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1 Triangle and its Properties 1. State which of the following triangles are possible. a) AB = 25cm, BC = 20cm, AC =15cm b) AB =8cm, BC = 8cm, AC = 80m c) PQ = 17cm, QR = 10 cm, PR = 10 cm d) PQ =3cm, QR=4cm, PR =5cm 2. Find out which of these are triangles. a) R = 100, P = 70, Q = 30 b) A = 5, B = 170, C= 5 c) A = 100, B = 100, C = The following triplets form the length in cm of the sides of a triangle. State which of them are right-angled triangles. (a) 8,10,6 (b) 15, 8, 7 (c) 9, 60, The square of the hypotenuse of an isosceles right-angled triangle is 72 sq cm. What is the length of each side? 5. The roof of a building is 8 m high. A rope is tied from the roof to a peg on the ground 6m away from the wall. What is the minimum length of the rope? 6. The length and breadth of a room are 3 m and 4 m. What is the length of the largest metallic rod that can be placed on the floor? 7. Ashok fixed a triangular tent of height 3 m. He tied the ends of the tents to two pegs fixed on the ground 8 m apart. What is the length of the tent from peg to peg? 3m Peg1 8m Peg 2 8. The angles of a triangle are in ratio 1:2: 3. Determine three angles. What type of triangle is it according to (i) angles (ii) sides? 9. One acute angle of a right-angled triangle measures 14 less than other acute angle. Find the measure of each angle. 10. In the adjoining figure, sides BC, CA and AB of a ABC are produced to form exterior angles 4, 5 and 6, show that = A 1 B C

2 11. Neha walks 12m west and then 5m north. How far is she away from her initial position? 12. Find the length of the diagonal of a square with each side of measure 5m. I VERY SHORT ANSWER QUESTIONS 1. In an isosceles triangle, one of the base angles is 55, find the vertical angle 2. Calculate the length of unknown side. S 13 cm T U 5 cm 3. The measure of the sides of a triangle is 4 cm, 12 cm, and 13 cm. Determine whether it is right angled triangle or not? 4. Find all angles of an equilateral triangle. 5. The angles of a triangle are (x-40), (x-20) and (x/2-10). Find the value of x. II FILL IN THE BLANKS: 1. The circumcentre of a triangle is the point of concurrence of 2. The point common to all the medians of a triangle is called its 3. All the three medians of a equilateral triangle are 4. The interior of the angle with the boundary is called. 5. The point common to all the altitudes of a triangle is called its. III TRUE FALSE 1. All angles of a triangle are less than 60º. 2. In a scalene triangle, all sides are unequal. 3. An exterior and the interior adjacent angle form a linear pair. 4. Two angles in a triangle are right angles. 5. Hypotenuse is the side which is opposite to the right angle. IV MULTIPLE CHOICE QUESTIONS 1. If two acute angles of a right triangle are equal, then each acute angle is: (a) 45 (b) 60 (c) One angle of a triangle is equal to the sum of the other two angles, then the type of the triangle is: (a) acute triangle (b) right triangle (c) obtuse triangle 3. In triangle ABC, C = A and BC = 17cm,then AB equals: (a) 14 cm (b) 7 cm (c) 17 cm 4. If AD is the median of equilateral triangle ABC, then: (a) 3AB 2 = 4AD 2 (b) 2AB 2 = 3AD 2 (c) AB 2 = 2AD 2 5. An exterior angle of a triangle is equal to 130º and the two interior opposite angles are equal. Each of these angles is equal to: (a) 55º (b) 65º (c) 52.5º

3 V MULTIPLE CHOICE QUESTIONS Tick the correct answer in each of the following: 1. What is the measure of each angle of an equilateral triangle? (a) 30 (b) 60 (c) 75 (d) If one angle of a right triangle is 60, the other two angles are: (a) 60, 60 (b) 90, 30 `(c) 80, 40 (d) none of these 3. If two angles of a triangle measure 40, 70, then measure of third angle is: (a) 80 (b)70 (c)60 (d)50 4. If one angle of a triangle has measure 80 and the other two angles are equal, then measure of each equal angles be: (a) 50,50 (b) 60, 40 (c) 70, 60 (d) 60,60 5. In an isosceles triangle, the angles opposite to equal sides are: (a) Acute (b) obtuse (c) equal (d) none of these. VI KEEPING IN TOUCH 1. If 2x + 3 = 5, then value of 3x + 2 is. 2. My younger sister's age today is 3 times, what it will be 3 years from now minus 3 times what her age was 3 years ago. Find her present age. 3. Seven times a number is 12 less than thirteen times the same number. Find the number 4. After 25 years, Rama will be 5 times as old as he is now. Find his present age 5. If 45 is added to half a number, the result is triple the number. Find the number. TRY THIS.

4 COMPARING QUANTITIES 1. If Rs. 250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages? 2. A school won 6 games this year against 4 games won last year. What is the percent increase? 3. If the price of milk increase from Rs. 30 per liter to Rs per liter. Find the percentage increase. 4. The number of illiterate person in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease? 5. An item has printed price Rs Due to reduction sale, it is sold for Rs. 400 Find the sale percent or reduction percent. 6. The price of sugar decreases from Rs. 20 Kg to Rs per kg. Find the decrease percentage. 7. A person buys a motorcycle for Rs and sells it for Rs Find his profit or loss percentage. 8. The cost of a flower vase is Rs If the shopkeeper sells it at a loss of 10% find the price at which it is sold. 9. A shopkeeper bought a chair for Rs 375 and sold it for Rs Find the gain percentage. 10. If selling price of an article is Rs. 420 and profit is 20%. Find its cost price. 11. A T.V. set of Rs is sold at a profit of 10%. Find its selling price. 12. If the selling price of an orange is Rs and there is a loss of 10%. Find the cost price per dozen. 13. Anita takes a loan of Rs at 15% per year as rate of interest. Find the interest she has to pay at end of one year. 14. Sandeep borrowed Rs for 4 years and Rs for 2 1 years from Sonia at the 2 same rate of interest. The total interest earned by Sonia is Rs Find the rate of interest. 15. Beena invested Rs at 18% p.a. interest from 17 June 2008 to 10 Nov. Calculate the interest. 16. Dipanker invested a sum of money from March 2008 at the rate of 12% p.a. If the interest received is Rs find the sum 17. What sum of money should be invested for 5 years t 8% p.a. to earn the same interest as Rs at 10% p.a. for 4 years? 18. If a farmer paid Rs as interest over 3 years at 2% per annum to a moneylender, how much loan had the farmer taken?

5 19. Two tables were sold at Rs. 990 each, one at a profit of 10% and the other at loss of 10% what are the cost prices of each of the tables? In this sale, did the seller make a profit or loss? What is the percentage of profit or loss? (Hint: In the first case, 110% of cost price is 990. In the second case 90% of cost price is 990) 20. On a certain sum the interest paid after 3 years is Rs. 450 at 5% rate of interest per annum. Find the sum. I VERY SHORT ANSWER QUESTIONS 1. Divide 72 in the ratio : Which ratio is larger? 1:2 or 13: What is the number whose 45% is 270? 4. The cost of 1 dozen pens is Rs. 36. Find the cost of 6 pens. 5. Convert each of the following pairs into percentages and find out which is more? 25 marks out of 30, 35 marks out of 40. II FILL IN THE BLANKS 1. The first term of the ratio is called. 2. Ratio is a number. It has.. unit :50 is equal to.% 4. Profit or loss is always reckoned on the 5. Sum borrowed is called III State whether the following are true or false 1. A ratio compares only two numbers % of 2500 is The percentage of 4:5 is 80 %. 4. The lowest term of 14.5% is 29/ The percentage of 4/5 is 80%. Keeping in touch:- 1. Caroline had 400 stamps in her collection. One-tenth of them were Indian stamps. Of the remaining, one-third was from Europe and 100 were from Africa. The rest were from United States of America. How many American stamps were there? 2.

Type of Triangle Definition Drawing. Name the triangles below, and list the # of congruent sides and angles:

Name: Triangles Test Type of Triangle Definition Drawing Right Obtuse Acute Scalene Isosceles Equilateral Number of congruent angles = Congruent sides are of the congruent angles Name the triangles below,