## two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their

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two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their angular points are equal

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1 month 2021-09-16T16:46:29+00:00 1 Answer 1 views 0

1. MATHS

In given figure two isosceles triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights.

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November 22, 2019

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Debabrata Sevda

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Let △ABC and △DEF be the given triangles such that AB=AC and DE=DF, ∠A=∠D

and

Area(△DEF)

Area(△ABC)

=

25

16

…….(i)

Draw AL⊥BC and DM⊥EF.

Now, AB=AC,DE=DF

AC

AB

=1 and

DF

DE

=1

AC

AB

=

DF

DE

DE

AB

=

DF

AC

Thus, in triangles ABC and DEF, we have

DE

AB

=

DF

AC

and ∠A=∠D [Given]

So, by SAS-similarity criterion, we have

△ABC∼△DEF

Area(△DEF)

Area(△ABC)

=

DM

2

AL

2

25

16

=

DM

2

AL

2

[Using (i)]

DM

AL

=

5

4

Hence, AL:DM=4:5…..

……i hope it’s helpful for u……