Question

in figure 3.59 point D and E are on side BC of triangle ABC such that BD is equal to CE and AD is equal to show that triangle ABC is congruent to triangle A C E​

Answer 1

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student-name Ashmit Raj asked in Math

D and E are points on side BC of a △ABC such that BD=CE and AD = AE. Show that

△ABD ≅△ACE.

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student-name Shrika Bharadwaj answered this

71 helpful votes in Math, Class XI-Science

If AD=AE

so ADE is an isoscelous triangle

So...angle ADE=angle AED

....angle ADB=angleAEC

therefore..bith triangles are congurent by SAS

AD=AE

angleADB=angleAEC

BD=EC

Answer 2

solution:-

given by:- D and E are on side BC of ΔABC, such that BD=CE and AD=AE

》Prove :- D and E are the point on side BC of a triangle ABC such that BD = CE and AD= AE

WE HAVE ,

》 AD = AE

》=> ∠ADE = ∠AED ........(1) ( angle opposite side)

now,

》 ∠ADB + ∠ADE = 180

》=> ∠ADB = 180-∠ADE

》 = 180 - ∠AED [ FROM EQ(1)]

》in triangle ABD and triangle ACE ,

》 => BD = CE

》=> AD = CE

》 [ΔABD≅ΔACE. ] proved

■I HOPE ITS HELP■