In the adjoining figure , AD is the bisector of BAC and AD EC. Prove that AC = AE . ~Thanks in advance ! ♡

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

                                 Given

                                   Definition of Bisector

                                              Given

                                   Alternate Interior Angles Theorem*

                                  Corresponding Angles Theorem*

                                  Substitution

                                   Substitution

                                             Isosceles Theorem Converse

*Please refer to the attachment below.

Let me know if you have any questions!

In the given figure AD is internal bisector of angle A and CE is parallel to DA. If CE meets BA produced at E.

to prove :AC=AE

<BAC + <EAC = 180° ( Straight line)

In triangle ACE

<ACE + <AEC + <EAC = 180° (sum ofangles of Triangle)

Equating both

<BAC + <EAC = <ACE + <AEC + <EAC

=<BAC = <ACE + <AEC.......... Eq 1

<BAD = (1/2) <BAC

<BAD = <AEC so (AD || CE)

we get

<AEC = (1/2) <BAC

putting this in eq 1

=<BAC = <ACE + <AEC Eq1

<BAD = (1/2) <BAC

<BAD = <AEC (AD || CE)

=<AEC = (1/2) <BAC

<AEC=<ACE=1/2 <BAC

: AC = AE

hence proved.

answer: approximately 206 bones

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