Ask a Doubt
Request a call back

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

CBSE Class 9 Answered

In ΔABC, AB = AC, A = 36°. If the internal bisector of C meet AB at D, prove that AD = BC.
Asked by Topperlearning User | 06 Dec, 2013, 10:43: AM
answered-by-expert Expert Answer

 

AB = AC

C = B [angles opposite to equal sides are equal]

In ABC A + B + C = 180o [Angle sum property of ]

36o   + 2C = 180o

2C = 144o

C = 72o

DCA =

DCA = DAC = 36o

AD = CD [sides opposite to equal angles are equal] … (i)

In CDB

AB C + C + CDB = 180o

72o + 36o + CDB = 180o

CDB = 180o - 72o - 36o

CDB = 72o

CDB = DBC = 72o

BC = CD [sides opposite to equal angles are equal] … (ii)

AD = BC (Using (i) and (ii))

Answered by | 06 Dec, 2013, 12:43: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
triangle ABC is an equilateral triangle, AB = 6cm. the points P,Q and R are midpoints of AB BC, CA respectively . the perimeter of □ PBCR is
question image
Asked by ghodage | 12 Dec, 2023, 07:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
the area of an equilateral triangle is 49√3 sq.cm, it's perimeter is
Asked by vijaykasaudhan913 | 10 Dec, 2023, 04:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
M is a point inside a square ABCD. AMCD is equilateral triangle and MC cuts diagonal DB at E. Then, ZBEC=..... (1) 75° (3) 105° (2) 90° (4) 60°
Asked by Krishna962511 | 23 Jan, 2023, 10:41: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In fig. 12.116 , T is a point on the side QR of ∆ PQR and S is a point such that RT=St. Prove that PQ+PR>QS
Asked by shivendrasinghfauzdar | 09 Oct, 2021, 11:30: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
In the figure, ABCD is a square and PAB is a triangle such that AQ = BR. Prove that DPQR is an isosceles triangle.
Asked by thebeatinbrat | 01 Oct, 2021, 08:56: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
If the vertex angle of an isosceles triangle is 50° ,find the other angels   
Asked by chikkammac24212 | 21 Aug, 2019, 07:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
show that BX=CY.
question image
Asked by shubham0kumar24 | 19 May, 2019, 12:44: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
AD is an altitude of an isosceles triangle ABC in which AB=AC.Show that  ( i )AD bisects BC (ii) AD bisects angle A.
Asked by Nagu.sahukar1543 | 14 Nov, 2018, 08:11: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
If the segments drawn perpendicular to the two sides of a triangle from the mid point of the third side be congruent and equally inclined to the third side, prove that the triangle is isosceles.
Asked by Topperlearning User | 10 Aug, 2017, 01:53: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
If the altitudes from two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.
Asked by Topperlearning User | 10 Aug, 2017, 01:56: 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
×