Opening ExerciseThe Angle Bisector Theorem states:In AABC, if the angle bisector ofLA meets side BC at point D, thenBD:CD = BA:CA.We are going to fill in the missing reasons of the proof of the Angle Bisector Theorem.Given: AD is the angle bisector of LABDProve:CDBACAStatementsReasons1.AD is the angle bisector of LA1.2.21= L22.Draw CE || to AB where E is the point of 3.intersection of AD. (Label 2CED as 23)3.4.22 =L34.5.L4 55.6.ACDEO ABDA6.BDВА7.7.CDСЕ8.8.9.AACE is isosceles9.10.CA CE10.BDBA11.11.CDCA

Answered: Image /qna-images/answer/51a90cdb-c1bf-4ad3-93b7-fb20ac75f8b9.jpg

Answered: Statements Reasons AD is the angle…

Statements Reasons AD is the angle bisector of LA 2122 2. Draw CE || to AB where E is the point of 3. intersection of AD. (Label 2CED as 43) 3. 22 L3 4. 5. L4 L5 5. 1, 1, 2. 4.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter3: Triangles

Section3.3: Isosceles Triangles

Problem 24E: In concave quadrilateral ABCD, the angle at A measures 40. ABD is isosceles, BC bisects ABD, and DC...

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Question

Opening Exercise
The Angle Bisector Theorem states:
In AABC, if the angle bisector of
LA meets side BC at point D, then
BD:CD = BA:CA.
We are going to fill in the missing reasons of the proof of the Angle Bisector Theorem.
Given: AD is the angle bisector of LA
BD
Prove:
CD
BA
CA
Statements
Reasons
1.
AD is the angle bisector of LA
1.
2.
21= L2
2.
Draw CE || to AB where E is the point of 3.
intersection of AD. (Label 2CED as 23)
3.
4.
22 =L3
4.
5.
L4 5
5.
6.
ACDEO ABDA
6.
BD
ВА
7.
7.
CD
СЕ
8.
8.
9.
AACE is isosceles
9.
10.
CA CE
10.
BD
BA
11.
11.
CD
CA

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