Ask a Doubt
Request a call back

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

CBSE Class 9 Answered

If two isosceles triangles have a common base, then the line joining their vertices bisects the base at right angles.
Asked by Topperlearning User | 10 Aug, 2017, 12:44: PM
answered-by-expert Expert Answer


ABC and DBC are two isosceles triangles with the common base, BC.

In ABD and ACD

AB = AC;

BD = CD;

AD = AD

ABD  ACD             (SSS congruence rule)

 
BAE = CAE                    (c.p.c.t)

In ABE and ACE

AB = AC;

BAE = CAE ;
  
  
AE = AE
 
ABE  ACE                                        (SAS congruence rule)

BEA = CEA and BE = EC                   (c.p.c.t)

BEA + CEA = 180o                                 (linear pair)

2BEA = 180o

  BEA = 90o

BEA = 90o = CEA

 
Hence, AD bisects the base BC at right angles.
Answered by | 10 Aug, 2017, 02:44: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
file
question image
Asked by maheshpatil2067 | 14 Jan, 2024, 04:36: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
solution
question image
Asked by harshitpal2115 | 30 Dec, 2023, 02:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
be and CF are two traiangle equal altitude of triangle abc using rhs congruence rule prove that the triangle abc is isosceles
Asked by arahant2008 | 07 Oct, 2021, 09:38: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
in an isosceles triangle ABC with AB=AC, the bisectors of angleB and angle C intersect each other at o. Join A at O. show that Ob= OC that
question image
Asked by sharan192006 | 10 Sep, 2020, 03:27: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
How to proove RHS congruence 
Asked by Nimmi | 26 Jan, 2019, 05:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In the given figure, BAAC and DEEF such that BA = DE and BF = DC. Prove that AC = EF.
Asked by Topperlearning User | 10 Aug, 2017, 12:35: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
ABC is an isosceles triangle with AB = AC. Bisectors of B and C intersect at O. Prove that BO = CO and AO bisects BAC.
Asked by Topperlearning User | 10 Aug, 2017, 12:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
ABCD is a square, X and Y are the points on the sides AB and DC respectively such that BY = CX. Prove that CY = BX and CBY = BCX.
Asked by Topperlearning User | 10 Aug, 2017, 12:44: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In an isosceles triangle, prove that the altitude from the vertex divides the triangle into two congruent triangles..
Asked by Topperlearning User | 10 Aug, 2017, 12:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
AD is the median of ABC. If BL and CM are drawn perpendiculars on AD produced, prove that BL= CM.
Asked by Topperlearning User | 10 Aug, 2017, 12:36: PM
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
×