Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

One angle of a triangle is equal to one angle of another triangle and the bisectors of these equal angles divide the opposite sides in the same ratio. Prove that the triangles are similar.( I want to know how this id directly assumed during the proof: the ratio of the corresponding sides=the ratio of the bisected side)
Asked by sajal2402 | 12 Feb, 2019, 10:36: AM
answered-by-expert Expert Answer
Angle bisector theorem :- anglar bisector of an angle of triangle divides the opposite side in same ratio as their sides of the smae angle.
 
In ΔABC, AD is bisector of begin mathsize 12px style angle end styleB , hence begin mathsize 12px style fraction numerator B D over denominator D C end fraction equals space fraction numerator A B over denominator A C end fraction end style
In the figure, In triangles ABC and PQR, begin mathsize 12px style angle end styleB = begin mathsize 12px style angle end styleP .  AD and PS are respective angular bisector.
then we have begin mathsize 12px style fraction numerator B D over denominator D C end fraction equals space fraction numerator A B over denominator A C end fraction end style  ...........................(1)
begin mathsize 12px style fraction numerator Q S over denominator S R end fraction space equals space fraction numerator P Q over denominator P R end fraction end style .............................(2)
Given : bisectors of begin mathsize 12px style angle end styleB and begin mathsize 12px style angle end styleP divides the opposite side in same ratio,  hence begin mathsize 12px style fraction numerator B D over denominator D C end fraction equals space fraction numerator Q S over denominator S R end fraction end style .........................(3)
By comparing (1), (2) and (3), we have begin mathsize 12px style fraction numerator A B over denominator A C end fraction equals fraction numerator P Q over denominator P R end fraction end style..........................(4)
In ΔABC and ΔPQR, begin mathsize 12px style angle end styleB = begin mathsize 12px style angle end styleP and the sides of these equal angles are in same ratio.  Hence ΔABC and ΔPQR are similar triangles
Answered by Thiyagarajan K | 12 Feb, 2019, 11:17: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
2/x+2/3y=1/6; 3/x+2/y=0
Asked by aditikaldate7 | 21 Apr, 2024, 03:16: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
ABCD is a rectangle in which diagonal AC is equals to 17 cm angle BCA is equals to thitha and sin theta is equals to 8/17 find the area of rectangle ABCDE (ii) the perimeter of rectangle ABCD
Asked by pathaksuman622 | 21 Apr, 2024, 11:56: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents P and Q intersect at a point T. Find the length of the tangent TP.
Asked by yalagondanikhil | 16 Apr, 2024, 12:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
if one of the zeroes of quadratic polynomial F(x) = 4x² - 8kx - 9 is equal in magnitude but opposite in sign, find K
Asked by rrajansinghakb199 | 08 Apr, 2024, 05:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
express 15.265 in p/q form?
Asked by nagalaxmidurgarao937 | 08 Apr, 2024, 01:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
the poles AB and CD of different heights are standing vertically on the ground level from a point P on the line joining the foots of the pole on the level of ground the angle of elevation to the top of the pole are founded to be complementary the of the CD and the distance PD 20√3m and 20m respectively if the BP is 10m then find the length of AB and the distance AC between the tpo of the poles
Asked by mraniruddha03 | 02 Apr, 2024, 06:44: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
from the pair of linear equations in the following problems and find their solution graphically 10 students of class 10 to part in a mathematic quiz if the number of girls is for more than the number of boys find the number of boys and girls who took part in the quiz
Asked by muttenenimalleswarrao | 29 Mar, 2024, 08:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
maths
question image
Asked by sonawnerohan01 | 23 Mar, 2024, 12:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
The distance of the point (5,-2) from x-axis will be :-
Asked by pathakvaishnavi9139 | 23 Mar, 2024, 10:45: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
income of families locality are given. find the mode of the data (income in rupees)=1-200,201-400,401-600,601-800,801-1000 and number of families are 7,10,16,12,3
question image
Asked by mustafahssn786 | 23 Mar, 2024, 06:25: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×