Triangles Exercise 10-4



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Exercise 10.1 Exercise 10.2 Exercise 10.3

Q1 In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is longest? Give reason for your answer.

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Q2 Show that in a right angled triangle, the hypotenuse is the longest side.

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Q3 PQR is a right angle triangle at Q and PQ : QR = 3:2. Which is the least angle.

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Q4 In ∆ ABC, AB = 8 cm, BC = 5.6 cm and CA = 6.5 cm. Which is (i) the greatest angle ? (ii) the smallest angle ?

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Q5 In ∆ABC, ∠A = 50°, ∠B= 60°, Arrange the sides of the triangle in ascending order.

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Q6 In figure given alongside, ∠B = 30°, ∠C = 40° and the bisector of ∠A meets BC at D. Show
(i) BD > AD
(ii) DC > AD
(iii) AC > DC
(iv) AB > BD

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Q7 (a) In the figure (1) given below, AD bisects ∠A. Arrange AB, BD and DC in the descending order of their lengths.
(b) In the figure (2) given below, ∠ ABD = 65°, ∠DAC = 22° and AD = BD. Calculate ∠ ACD and state (giving reasons) which is greater : BD or DC ?

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Q8 (a) In the figure (1) given below, prove that (i) CF> AF (ii) DC>DF.
(b) In the figure (2) given below, AB = AC. Prove that AB > CD.
(c) In the figure (3) given below, AC = CD. Prove that BC < CD.

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Q9 (a) In the figure (i) given below, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.

(b) In the figure (ii) given below, D is any point on the side BC of ∆ABC. If AB > AC, show that AB > AD.


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Q10 (i) Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer,
(ii) Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
(iii) Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.

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