I am going to prove that ray AF is an angle bisector E of the triangle DAE using the Side-Angle-Side Triangle Congruence Theorem. Segments DF and EF are congruent because F was constructed to be the midpoint of DE. Segments DA and EA are congruent because they are radii of the same circle. Because triangle DAE is isosceles, angle D is congruent to angle E, so triangles AEF and ADF are congruent by the Side-Angle-Side Triangle Congruence Theorem. Therefore, angle EAF is congruent to angle DAF because they are corresponding parts of congruent triangles. The construction does create an angle bisector. II II

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Place them in order
ots about Paral.
14 of 22
N
em
Write a proof of why ray AF must be an angle bisector of the triangle DAE.
I am going to prove that ray AF is an angle bisector
E of the triangle DAE using the Side-Angle-Side
Triangle Congruence Theorem.
Segments DF and EF are congruent because F
was constructed to be the midpoint of DE.
F
Segments DA and EA are congruent because they
are radii of the same circle.
Because triangle DAE is isosceles, angle D is
congruent to angle E, so triangles AEF and ADF are
congruent by the Side-Angle-Side Triangle
Congruence Theorem.
Therefore, angle EAF is congruent to angle DAF
because they are corresponding parts of congruent
triangles. The construction does create an angle
bisector.
Sign out
Transcribed Image Text:ots about Paral. 14 of 22 N em Write a proof of why ray AF must be an angle bisector of the triangle DAE. I am going to prove that ray AF is an angle bisector E of the triangle DAE using the Side-Angle-Side Triangle Congruence Theorem. Segments DF and EF are congruent because F was constructed to be the midpoint of DE. F Segments DA and EA are congruent because they are radii of the same circle. Because triangle DAE is isosceles, angle D is congruent to angle E, so triangles AEF and ADF are congruent by the Side-Angle-Side Triangle Congruence Theorem. Therefore, angle EAF is congruent to angle DAF because they are corresponding parts of congruent triangles. The construction does create an angle bisector. Sign out
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