Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises: 38

Answer

To prove that $\angle B\cong\angle E$, we would use the theorem that the total sum of 3 angles in any triangles equals $180^{\circ}$.

Work Step by Step

We know the sum of 3 angles in any triangles equals $180^{\circ}$. Therefore, $\angle A+\angle B+\angle C=\angle D+\angle E+\angle F=180^{\circ}$ So, $\angle A+ \angle B+ \angle C\cong\angle D+\angle E+ \angle F$ But, we already know that $\angle A\cong\angle D$ and $\angle C\cong\angle F$. Therefore, it follows that $\angle B\cong\angle E$ In conclusion, to prove that $\angle B\cong\angle E$, we would use the theorem that the total sum of 3 angles in any triangles equals $180^{\circ}$.
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