Math Assignment Ch-6 Class X | Triangle

Maths. Assignment Class X Chapter 6 : Triangle

Extra questions of class x, chapter 6, extra questions of triangle chapter 6, class x

Important Result : 

Internal bisector of angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.    In Triangle ABC, if AD is the bisector of ∠A then \[\frac{AB}{AC}=\frac{BD}{DC}\]

For detailed study and basic concepts related to the similarity of triangles: Click Here

Solve the following questions

Question 1: Q. 1. PA, QB and RC are each perpendicular to AC then

Question 2: If the bisector of an angle of  triangle bisects the opposite side, then prove that the triangle is isosceles.

Question 3: O is any point inside a triangle ABC. The bisectors of ∠AOB, ∠BOC and ∠COA meet the side AB, BC and CA in points D, E, F respectively.  Show that AD X BE X CE = BD X EC X FA

Question 4: In triangle ABC, AD is the internal bisector of ∠A which meets BC at point D.  Prove that:

Question 5: In the given figure express x in terms of a, b, c

Question 6: Q6 The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. Find the ratio of their corresponding heights? What is the ratio of their corresponding median.

Question 7: In quadrilateral ABCD,  ∠B = 90o  If AD2 = AB2 + BC2 = CD2  Prove that ∠ACD = 90o

Question 8: In the given figure PQR,   S and T trisects the side QR of a right triangle PQR.  Prove that 8PT2 = 3PR2 + 5PS2

Question 9: Triangle ABC is right angled at B ,  D is the mid- point of BC. Prove that AC2 =  4AD2 - 3AB2

Question 10: In triangle ABC, AD ⟂ BC and point D lies on BC such that 2BD = 3CD, Prove that 5AB2 = 5AC2 +BC2

Question 11: △ABC is right angled at C. Let BC = a, CA = b, BC = c, and let p be the length of perpendicular from C on AB Prove That :

Question 12: In △ABC, P and Q are the points on sides CA and CB respectively, which divides these sides in 2 : 1. Prove that  (i) 9AQ2 = 9AC2 + 4BC2 (ii) 9BP2 = 9BC2 + 4AC2 (iii) 13AB2  = 9(AQ2 + BP2)

Question 13: In △ABC, AC > AB,  D is the mid - point of BC and   AE⟂BC . Prove that :

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