PDF 1) Given: 1 And 4 Are Supplementary. Prove

Feb 11 AG Quiz Review Proofs.notebook 4 February 11, 2016 Sep 86:42 PM 4)Complete the proof by filling in the blanks. Given: <W and <V are congruent and supplementary3. Given: ∠1 and ∠2 are supplementary. ∠1 ≅∠2. Prove: ∠1 and ∠2 are right angles. Statements Reasons 1.∠1 and ∠2 are supplementary. ∠1 ≅∠2 1.Given 2.m∠1 + m∠2 = 180° 2.Definition of Supplementary Angles 3.m∠1 = m∠2 3.Definition of ≅angles. 4.m∠1 + m∠1 = 180° 4.Substitution 5.2 m∠1 = 180° 5.SimplifyWrite a paragraph proof to prove that ∠2 and ∠3 are complementary given that ∠1 and ∠2 are complementary, and m∠1 = m∠3. It is given that ∠1 and ∠2 are complementary. By the definition of complementary angles, m∠1 + m∠2 = 90°.Because ∠1 and ∠2 are supplementary and ∠3 and ∠4 are supplementary, m∠1 + m∠2 = 180° and m∠3 + m∠4 = by the defi nition of supplementary angles. By the Transitive Property of Equality, m∠1 + m∠2 = m∠3 + m∠ we are given that ∠1 ≅ ∠4, by defi nition of congruent m1 = ∠4. Therefore, by the SubstitutionGiven: m 1 + m 2 = m 4 Prove: m 3 + m 1 + m 2 = 180° Paragraph Proof: It is given that m 1 + m 2 = m 4. 3 and 4 are supplementary by the Linear Pair Theorem. So m 3 + m 4 = 180° by definition. By Substitution, m 3 + m 1 + m 2 = 180°. Statements Reasons 1. m 1 + m 2 = m 4 1. Given 2. 3 and 4 are supp. 2.

Common Segment Theorem Vertical Angle Theorem

October 10, 2011 1. Given: m 1 = 24, m 3 = 24 1 comp. 2 3 comp. 4 Prove: 2 = 4 Statement Reason 1. _____ 1.I am so confused on proofs! This is what i have so far: ( I would appreciate if you could tell me if it is wrong or right!) a. m<1 = m<2 : given b. <1 is supplementary to <2. : Definition of supplementary angle c. m<1 + m<2 = 180degrees :Linear pair postulate d. m<1 + m<1 = 180degrees 2(m<1) = 180degrees : (this is one step. but the 2(m<1) = 180degrees is right below the first one2. m<2 + m<3 = 180 2. Definition of Supplementary . 3. m<1 + m<2 = 180 3. Linear Pair Postulate . 4. m<1 + m<2 = m<2 + m<3 4. Substitution POEAnswer to Directions: Complete each proof. 1. Given: m/4+ m/7 =180 Prove: c || d Statements Reasons 1. M24 +m< 7 = 180. 1. aiven 2. 24 ~ 46 2 .) 3. Mc 4 =

1.4.4 Quiz - Week Four: Mathematical Proof Flashcards

102 Chapter 2 Reasoning and Proofs Writing a Two-Column Proof Prove this property of midpoints: If you know that M is the midpoint of AB — , prove that AB is two times AM and AM is one-half AB. Given M is the midpoint of AB — . AMB Prove AB = 2AM, AM = 1— 2 AB STATEMENTS REASONS 1. M is the midpoint of AB — 1. Given 2. AM — ≅ MB — 2. De! nition of midpointSAMPLE ANSWERS: OPTIONAL PROOF PRACTICE (3.5 Quiz), Page 1 of 2 Given: l || m 1 . Prove: 2 & 5 are supplementary (Hint: Scribble out all angles EXCEPT 2, 4, and 5) Statements Reasons l || m 1. Given 2. 4 and 5 are supplementary 2. Consecutive Interior. Angles Thm 3. m 4 + m 5 = 180o 3. Definition of supplementary s 4. 2 # 4 4.110 Chapter 2 Reasoning and Proofs Using the Vertical Angles Congruence Theorem Write a paragraph proof. Given ∠1 ≅ ∠4 Prove ∠2 ≅ ∠3 Paragraph Proof ∠1 and ∠4 are congruent. By the Vertical Angles Congruence Theorem, ∠1 ≅ ∠2____ 13. Fill in the blanks to complete the two-column proof. Given: ∠1 and ∠2 are supplementary. m ∠1 = 135 ° Prove: m ∠2 = 45 ° Proof: Statements Reasons 1. ∠1 and ∠2 are supplementary. 1. Given 2. [1] 2. Given 3. m ∠1 + m ∠2 = 180 ° 3. [2] 4. 135 ° + m ∠2 = 180 ° 4. Substitution Property 5. m ∠2 = 45 ° 5. [3] a. [15 is supp. to 4 Prove: 3 5 Statements Reasons 1. 3 is supp. to 4 1. 2. m 3 + m 4 = 180 2. 3. m 3 = 180 - m 4 3. 4. 5 is supp. to 4 4. 5. m 5 + m 4 = 180 5. 6. m 5 = 180 - m 4 6. 7. 3 5 7. Congruent Supplements Theorems: If angles are supplementary to the same angle, then they are congruent.

Download PDF