Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises - Page 129: 15


Using method ASA for 2 congruent pairs of angles and one included pair of sides, we can prove that $\triangle ABC\cong\triangle DBC$.

Work Step by Step

Since $\vec{CB}$ bisects $\angle ACD$, two resulting angles of this bisect would be equal with each other. That means $\angle 3\cong\angle 4$. It is also mentioned that - $\angle A\cong\angle D$ - $\overline{AC}\cong\overline{CD}$ We now have 2 angles and the included side of $\triangle ABC$ are congruent with 2 angles and the included side of $\triangle DBC$. Therefore, according to method ASA, $\triangle ABC\cong\triangle DBC$.
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