[tex] \underline{ \underline{ \text{Question}}} : [/tex] In the adjoining figure , AD is the bisector of [tex] \angle[/tex] BAC and AD [tex] \parallel[/tex] EC. Prove that AC = AE .
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![[tex] \underline{ \underline{ \text{Question}}} : [/tex] In The Adjoining Figure , AD Is The Bisector](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/piHjS4WosGDFo2YtFkpCCbTNJgA0qR7y.jpeg)
Answers
Answer:
See Below.
Step-by-step explanation:
Statements: Reasons:
[tex]1)\text{ } AD\text{ bisects } \angle BAC[/tex] Given
[tex]2)\text{ } \angle BAD \cong \angle CAD[/tex] Definition of Bisector
[tex]\displaystyle 3) \text{ } A D \parallel E C[/tex] Given
[tex]\displaystyle 4)\text{ } \angle CAD\cong \angle ACE[/tex] Alternate Interior Angles Theorem*
[tex]\displaystyle 5) \text{ } \angle BAD\cong \angle BEC[/tex] Corresponding Angles Theorem*
[tex]6)\text{ } \angle CAD\cong \angle BEC[/tex] Substitution
[tex]7)\text{ } \angle ACE\cong\angle BEC[/tex] Substitution
[tex]\displaystyle 8)\text{ } AC = A E[/tex] Isosceles Theorem Converse
*Please refer to the attachment below.
Let me know if you have any questions!
![[tex] \underline{ \underline{ \text{Question}}} : [/tex] In The Adjoining Figure , AD Is The Bisector](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/4goVhWYPdYE9FbTfXUTv2Tgrf7fpO48f.jpeg)
Answer:
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.
![[tex] \underline{ \underline{ \text{Question}}} : [/tex] In The Adjoining Figure , AD Is The Bisector](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/DUiKfsiSMz5PjGlzNs0UsKr595CheKuT.jpeg)
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Answer:
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Step-by-step explanation:
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Answer:
1.05(b) = 0.97(b)
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Answers
Answer:
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Answer:
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