Home
Class 10
MATHS
In Delta ABC and Delta PQR , angle ABC ...

In `Delta ABC` and ` Delta PQR , angle ABC cong angle PQR ` eg BD and seg QS are angles bisectors . If `(l(AD))/(l(PS)) = (l(DC))/(l(SR)) = " then " Delta ABC ~ Delta PQR`
` (##NVT_21_MAT_P2_X_C09_E01_002_S01.png" width="80%">

Text Solution

Verified by Experts

` (l(AD))/(l(PS))= (l(DC))/(l(SR))`
` :. ` by alternando
` (l (AD))/(l(DC))= (l(PS))/(l(SR))" "` … (1)
In ` Delta ABC,`
BD is the bisector of ` angle ABC`
` (l(AB))/(l(BC))=(l(AD))/(l(DC))" "` …(2) [ Angle bisector theorem of Delta]
In `Delta PQR,`
ray QS is the bisector of ` angle PQR `
` (l(PQ))/(l(QR)) = (l(PS))/(l (SR))" "` ...(3) [ Angle biector theorem if Delta ]
` :. ` from (1),(2),(3)
` (l(AB))/(l(BC)) = (l(PQ))/(l(QR))`
` :. ` by alternando
` (l(AB))/(l(PQ))= (l(BC))/(l(QR))" "` ...(4)
In `Delta ABC and Delta PQR`,
` (l(AB))/(l(PQ)) = (l(BC))/(l(QR))" "` ...[ From (4)]
` angle ABC cong angle PQR " "` ...(Given)
` :. Delta ABC ~ Delta PQR " "` ... (SAS test of similarity )
Promotional Banner

Topper's Solved these Questions

  • CHALLENGING QUESTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE )|7 Videos

  • CHALLENGING QUESTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Choose the correct alternative :|3 Videos

  • CHALLENGING QUESTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLE FOR PRACTICE|22 Videos

  • CIRCLE

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Challenging Questions|10 Videos

Similar Questions

Explore conceptually related problems

In Delta ABC, angle ACB = 90^(@) ," seg "CD bot side AB and seg CE is angle bisector of angle ACB Prove : (AD)/(BD) = (AE^(2))/(BE^(2))

In Delta ABC and Delta PQR, angleB = angle Q, angleC = angle R . M is the mid-point of side QR. If AB : PQ = 7 : 4, then ("area " (Delta ABC))/("area " (Delta PMR)) is :

In a Delta ABC, angle B=100^(@), angle C=70^(@), AE _|_ BC & AD is angle bisector . Find angle EAD .

Delta ABC ,angle B external angle C meets at P angle A = 80 " then " angle BPC = ?

The perimeter of the triangle shown in figure. is (##NCERT_EXM_MAT_VI_C07_E01_015_Q01.png" width="80%">

In a Delta ABC, angle B = 2 angle C Angle bisector AD and BE intersect of O. AB = CD find angle ABC

In a Delta ABC , angle bisector of interior angle B and exterior angle C intersect at P . If angle A=70^(@) . Find angle BPC .

NAVNEET PUBLICATION - MAHARASHTRA BOARD-CHALLENGING QUESTIONS-SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Solve any one of the following subquestions :
  1. In Delta ABC and Delta PQR , angle ABC cong angle PQR eg BD and se...

    Text Solution

    |

  2. Solve any one of the following subquestions : Draw a circle with c...

    Text Solution

    |