University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2022
Views:

123

Pages:

8
Author:

Uszewskadndr

Connect Proofs to Section 2-4: Special Pairs of Angles Right Angle: An angle whose measure is 90. Straight Angle: An angle whose measure is 180. Complementary Angles: Two angles whose measures sum to 90. Supplementary Angles: Two angles whose measures sum to 180. Vertical Angles: The two non-adjacent angles that are created by a pair of intersecting lines. (They are across from one another.) Given: 1 and 2 are complementary Prove: ABC is a right angle. A B Statements 1 2 C Reasons 1. 1 and 2 are complementary 1. Given 2. m1 + m2 = 90 2. Definition of Complementary Angles 3. m1 + m2 = mABC 3. Angle Addition Postulate 4. mABC = 90 4. Substitution 5. ABC is a right angle. 5. Definition of a right angle. Given: DEF is a straight angle. Prove: 3 and 4 are supplementary D Statements 3 4 E F Reasons 1. mDEF is a straight angle. 1. Given 2. mDEF= 180 2. Definition of a straight angle 3. m3 + m4 = mDEF 3. Angle Addition Postulate 4. m3 + m4 = 180 4. Substitution 5. 3 and 4 are supplementary. 5. Definition of supplementary angles Vertical Angle Theorem: Vertical Angles are Congruent. Conditional: If two angles are vertical angles, then the angles are congruent. Given: Two angles are vertical angles. Hypothesis: Conclusion: Prove: The angles are congruent. Vertical Angle Theorem Proof Given: 1 and 2 are vertical angles. Prove: 1 @ 2 4 1 2 3 NOTE: You cannot use the reason “Vertical Angle Theorem” or “Vertical Angles are Congruent” in this proof. That is what we are trying to prove!! Vertical Angle Theorem Proof Given: Diagram Below 4 1 2 Prove: 1 @ 2 3 Statements 1. m1 + m3 = 180 m3 + m2 = 180 Reasons 1. Angle Addition Postulate 2. m1 + m3 = m3 + m2 2. Substitution **. m3 = m3 **. Reflexive Property 4. m1 = m2 4. Subtraction Property Proof Example Given: 2 @ 3; Prove: 1 @ 4 YOU CANNOT UNDER ANY CIRCUMSTANCES Statements Reasons 1. Given USE THE REASON 1. 2 @ 3 OF 2. Vertical Angles are Congruent 2. 2 @ “DEFINITION 1 VERTICAL ANGLES” 3. Substitution 3. 1 @ 3 IN A 4.PROOF!! You can also Vertical Angles are say Congruent 1 4 2 3 4. 3 @ 4 5. 4 @ 1 “Vertical Angle Theorem” 5. Substitution Given: Proof Example Prove: 1 @ 3 1 and 2 are supplementary; 1 3 and 4 are supplementary; 2 @ 4 2 3 4 Statements Reasons 1. 1 and 2 are supplementary 1. Given 3 and 4 are supplementary 2. m1 + m2 = 180 m3 + m4 = 180 2. Definition of Supplementary Angles 3. m1 + m2 = m3 + m4 3. Substitution 4. 2 @ 4 or m2 = m4 4. Given 5. m1 = m3 or 1 @ 3 5. Subtraction Property