Homework Help is Here – Start Your Trial Now!
Math
Geometry
PROOF 16) If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Given BAL BC Prove 21 and 22 are complementary. Two-Column Proof STATEMENTS 1. BALBC 2. LABC is a right angle. 3. m/ABC = 90° 4. m/ABC = mz1+mz2 5. 90° = m/1 + m22 6. 21 and 22 are complementary. Reasons Bank REASONS 1. 2. 3. 4. 5. 6. Angle Addition Postulate Transitive Property of Equality Definition of right angle V 2 Definition of complementary angles Definition of perpendicular lines

PROOF 16) If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Given BAL BC Prove 21 and 22 are complementary. Two-Column Proof STATEMENTS 1. BALBC 2. LABC is a right angle. 3. m/ABC = 90° 4. m/ABC = mz1+mz2 5. 90° = m/1 + m22 6. 21 and 22 are complementary. Reasons Bank REASONS 1. 2. 3. 4. 5. 6. Angle Addition Postulate Transitive Property of Equality Definition of right angle V 2 Definition of complementary angles Definition of perpendicular lines

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Question
**Proof Explanation** **Problem:** If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. **Given:** \(\overline{BA} \perp \overline{BC}\) **To Prove:** \(\angle 1\) and \(\angle 2\) are complementary. **Two-Column Proof** | **Statements** | **Reasons** | |------------------------------------------|-----------------------------------------------| | 1. \(\overline{BA} \perp \overline{BC}\) | 1. Given | | 2. \(\angle ABC\) is a right angle. | 2. Definition of perpendicular lines | | 3. \(m\angle ABC = 90^\circ\) | 3. Definition of right angle | | 4. \(m\angle ABC = m\angle 1 + m\angle 2\)| 4. Angle Addition Postulate | | 5. \(90^\circ = m\angle 1 + m\angle 2\) | 5. Transitive Property of Equality | | 6. \(\angle 1\) and \(\angle 2\) are complementary. | 6. Definition of complementary angles | **Diagram Explanation:** The diagram presents an angle \( \angle ABC \) with \(\overline{BA}\) forming a vertical line and \(\overline{BC}\) forming a horizontal line at point B, indicating that they are perpendicular. There are two angles, \(\angle 1\) and \(\angle 2\), which together make up \(\angle ABC\). **Reasons Bank:** - Angle Addition Postulate - Transitive Property of Equality - Definition of right angle - Definition of complementary angles - Definition of perpendicular lines - Given
Transcribed Image Text:**Proof Explanation** **Problem:** If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. **Given:** \(\overline{BA} \perp \overline{BC}\) **To Prove:** \(\angle 1\) and \(\angle 2\) are complementary. **Two-Column Proof** | **Statements** | **Reasons** | |------------------------------------------|-----------------------------------------------| | 1. \(\overline{BA} \perp \overline{BC}\) | 1. Given | | 2. \(\angle ABC\) is a right angle. | 2. Definition of perpendicular lines | | 3. \(m\angle ABC = 90^\circ\) | 3. Definition of right angle | | 4. \(m\angle ABC = m\angle 1 + m\angle 2\)| 4. Angle Addition Postulate | | 5. \(90^\circ = m\angle 1 + m\angle 2\) | 5. Transitive Property of Equality | | 6. \(\angle 1\) and \(\angle 2\) are complementary. | 6. Definition of complementary angles | **Diagram Explanation:** The diagram presents an angle \( \angle ABC \) with \(\overline{BA}\) forming a vertical line and \(\overline{BC}\) forming a horizontal line at point B, indicating that they are perpendicular. There are two angles, \(\angle 1\) and \(\angle 2\), which together make up \(\angle ABC\). **Reasons Bank:** - Angle Addition Postulate - Transitive Property of Equality - Definition of right angle - Definition of complementary angles - Definition of perpendicular lines - Given
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer