Elementary Geometry for College Students (6th Edition)

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

Chapter 1 - Section 1.2 - Informal Geometry and Measurement - Exercises - Page 18: 27


$\angle$5 is congruent to $\angle$6.

Work Step by Step

Let's call the unmarked angle, $\angle$7 (in the diagram, between angles 5 and 6). Because all right angles equal 90$^{\circ}$, we can add angles 5 and 7, creating m$\angle$5 + m$\angle$7 = 90$^{\circ}$. For the same reason (all right angles equal 90$^{\circ}$) we can add angles 6 and 7, creating m$\angle$6 + m$\angle$7 = 90$^{\circ}$. Using the Property of Substitution, m$\angle$5 + m$\angle$7 = m$\angle$6 + m$\angle$7 (since both sets of angles equal ninety degrees we can put them equal to each other). Using the Subtraction Property, we can subtract angle 7 from both sides of our equation, like this m$\angle$5 + m$\angle$7 - m$\angle$7 = m$\angle$6 + m$\angle$7 - m$\angle$7. This proves that m$\angle$5 = m$\angle$6. And lastly, using the Definition of Congruence $\angle$5 is congruent to $\angle$6.
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