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

Solution

Question 2:

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

Solution

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

Solution

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:

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 = 90^o  If AD² = AB² + BC² = CD²  Prove that ∠ACD = 90^o 

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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