Request a call back

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

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

In ABD and ACD

AB = AC;

BD = CD;

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

CBSE 9 - Maths
Asked by arahant2008 | 07 Oct, 2021, 09:38: PM
CBSE 9 - Maths
Asked by sharan192006 | 10 Sep, 2020, 03:27: PM
CBSE 9 - Maths
Asked by Nimmi | 26 Jan, 2019, 05:10: PM
CBSE 9 - Maths
Asked by Topperlearning User | 10 Aug, 2017, 12:35: PM
CBSE 9 - Maths
Asked by Topperlearning User | 10 Aug, 2017, 12:46: PM
CBSE 9 - Maths
Asked by Topperlearning User | 10 Aug, 2017, 12:44: PM