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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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Tickets for a dance recital cost $15 for adults and $7 for children. The dance company sold 253 tickets, and the total receipts
elixir [45]

Answer:

Adult tickets =125

Child tickets = 128

Step-by-step explanation:

Let the number of adult and children tickets sold be x and y respectively

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x+y= 253--------1

Since total sales/receipt is $2,771

And given that tickets for a dance recital cost $15 for adults and $7 for children hence

15x+7y= 2771-------2

Solving equation 1 and 2 simultaneously we have

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15x+7y= 2771----------2

Let us multiply equation 1 by 15 to get equation 3 to eliminate x and subtract equation 2 from 3

15x+15y=3795---------3

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0+8y=1024

8y= 1024

y= 1024/8

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So solve for x let us put y= 128 in equation 1

x+ 128=253

x=253-128

x= 125 tickets

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