2.5_Angle_Theorems

2.5_Angle_Theorems - Given 2 supp ‘s sum = 180° 3 sub B...

This preview shows pages 1–11. Sign up to view the full content.

Angle Theorems

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
If two angles form a linear pair, then they are supplementary.
Given: 1 & 2 are a linear pair Prove: 1 & 2 are supplementary 1 & 2 are a linear pair of angles formed by opposite rays BA and BC. Opposite rays form a straight angle so m ABC = 180°. By angle addition, m ABC = m 1 + m 2. Using substitution 180° = m 1 + m 2. Therefore by definition of supplementary angles, 1 & 2 are supplementary. 2 1 A B C

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
If two angles form a linear pair, then the sum of the angles is 180°.
Given: 1 & 2 are a linear pair Prove: m 1 + m 2 = 180° 1. 1 & 2 are a linear pair 2. 1 + 2 are supplementary 3. m 1 + m 2 = 180° statements 1. Given 2. Linear pair supp. 3. supp. ’s sum 180° 2 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Supplements of the same angle or congruent angles are congruent.
Given: A & B are supplementary C & B are supplementary Prove: A C 1. A & B are supp. C & B are supp. 2. m A + B = 180° m C + B = 180° 3. m A + m B = m C + m B statements 1.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Given 2. supp. ‘s sum = 180° 3. sub. B reasons C A 4. m A = m C 4. 5. A C 5. = Complements of the same angle or congruent angles are congruent. Given: A & B are complementary C & B are complementary Prove: A C 1. A & B are comp. C & B are comp. 2. m A + B = 90° m C + B = 90° 3. m A + m B = m C + m B statements 1. Given 2. comp. ’s sum = 90° 3. sub. B reasons C A 4. m A = m C 4. 5. A C 5. = Verticals angles are congruent. Given: A & B are vertical angles Prove: A C 1. A & C are vertical ’s 2. A & B are a linear pair C & B are a linear pair 3. A & B are supp. C & B are supp. statements 1. Given 2. Def linear pair 3. Linear pair supp. B reasons C D 4. A C 4. Supp. ’s A...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern