Elementary Geometry for College Students (5th Edition)

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

Chapter 1 - Section 1.6 - Relationships: Perpendicular Lines - Exercises: 28

Answer

1. Given 2. Definition 3. Given 4. Definition 5. Substitution 6. Substraction Property of Equality. 7. Substraction Property of Inequality 8. Addition Property of Equality 9. Transitive property of Inequality 10. Substitution 11. Definition

Work Step by Step

1. Given 2. The definition of complementary angles 3. Given 4. The definition of an acute angle 5. Substituting $m\angle 1$ in the equation (Statement 2.) 6. Subtracting $x$ from both sides. 7. Subtracting $x$ from all three sides in the inequality (Statement 4.) 8. Adding $90$ to all three sides in the equality (Statement 7.) 9. Transitive property of inequality (Statement 7. and 8.) As $0\lt 90-x$ and $90-x\lt90$, therefore $0\lt90-x\lt90$ 10. Substituting $90-x$ by $m\angle 2$ (Statement 6.) 11. Using the definition of an acute angle
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