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MA_775_DIABLO [31]
3 years ago
11

ABC is an isosceles triangle in which AC =BC.

Mathematics
2 answers:
Valentin [98]3 years ago
6 0

Answer:

Given ABC is an isosceles triangle with AB=AC .D and E are the point on BC such that BE=CD

  • Given AB=AC

∴∠ABD=∠ACE (opposite angle of sides of a triangle ) ....(1)

  • Given BE=CD

Then BE−DE=CD−DE

ORBC=CE......................................(2)

In ΔABD and ΔACE

∠ABD=∠ACE ( From 1)

BC=CE (from 2)

AB=AC ( GIven)

∴ΔABD≅ΔACE

So AD=AE [henceproved]

aev [14]3 years ago
3 0

Given:

ABC is an isosceles triangle in which AC =BC.

D and E are points on BC and AC such that CE=CD.

To prove:

Triangle ACD and BCE are congruent​.

Solution:

In triangle ACD and BCE,

AC=BC                  (Given)

AC\cong BC

\angle C\cong m\angle C                  (Common angle)

CD=CE                  (Given)

CD\cong CE

In triangles ACD and BCE two corresponding sides and one included angle are congruent. So, the triangles are congruent by SAS congruence postulate.

\Delta ACD\cong \Delta BCE           (SAS congruence postulate)

Hence proved.

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