Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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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.
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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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