2/11/16 Review for Proofs Quiz
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1 2/11/16 Review for Proofs Quiz EQ:Name some of the most common properties, theorems, and postulates used when performing proofs. MCC9 12.G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. MCC9 12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180o; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point Sep 8 5:10 PM 1
2 Two Column Proofs Complete the proof by filling in the blanks. : GK HJ Prove: GIK~ HIJ GK HJ <G <KGH GIK~ HIJ Corresponding angle theorem Corresponding Angles AA~ Sep 8 5:23 PM 2
3 : MQ OP Prove: ΔMNQ~PNO MQ OP <MNQ <ONP Vertical Angles <QMN <OPN Alternate Interior Angles ΔMNQ~ΔPNO AA~ Sep 8 6:11 PM Paragraph Proof Complete the following proof by filling in the blanks. : m<1 = m<3 Prove: m<aec = m<deb Proof : It is given that. m<1 = m<3 By the Reflexive Property we know that m<2 = m<2. So because of the Addition Property we can say, m<1 + m<2 =m<3 + m<2. By the, Angle Addition Postule m<1 + m<2 = m<aec. Also, by the Angle Addition Postulate, m<3 + m<2 = m<deb. By the, m<aec = m<deb. Sep 8 6:30 PM 3
4 Complete the proof by filling in the blanks. : <W and <V are congruent and supplementary Prove: <W and <V are right angles <W <V <W = <V <W & <V are supplementary <W + <V = 180 m<w + m<w = 180 or 2m<W = 180 Congruent angles have the same measure Definition of supplementary Substitution Property m<w = 90 Division Property m<v = 90 8) <W & <V are right angles 8) Definition of right angles Sep 8 6:42 PM Flow Proof Complete the proof by filling in the blanks. : <1 and <2 are supplementary; <3 and <4 are supplementary; <2 <4 Prove: <1 <3 <1 and <2 are supplementary <3 and <4 are supplementary <2 <4 m<1 + m<2 = 180 Definition of Supplementary m<3 + m<4 = 180 Definition of Supplementary m<1 + m<2 = m<3 +m<4 <2 = <4 Conguent angles have the same measure m<1 + m<2 = m<3 +m<2 <1 = <3 Substitution Property Subtration Property <1 <3 Angles with the same measure are congruent Sep 8 7:03 PM 4
5 Complete the proofs by filling in the blanks. : AB Prove: AC CD BD AB CD AB = CD Congruent segments have = length BC = BC Reflexive Property AB + BC = BC + CD Addition Property AB + BC = AC Segment Addition Postulate BC + CD = BD Segment Addition Postulate AC BD Substitution Property Sep 8 7:44 PM : a b; <1 <4 Prove: <2 <3 a b m<1 + m<2 = 180 Consecutive Interior Angles are supplemental m<3 + m<4 = 180 Consecutive Interior Angles are supplemental m<1 + m<2 = m<3 + m<4 <1 <4 m<4 + m<2 = m<3 + m<4 m<2 = m<3 Substitution Property Subtraction Property 8) m<2 m<3 8) Congruent Angles have = measure Sep 8 8:07 PM 5
6 8) : FG GH; JK KL; <F <J Prove: ΔFGH ~ ΔJKL FG GH; JK KL ΔFGH is isosceles Definition of isosceles Δ ΔJKL is isosceles <F <H; <J <L Definition of isosceles Δ Base angles of isosceles Δ are <F <J <H <J <H <L 8) ΔFGH ~ ΔJKL 8) AA~ Sep 8 8:28 PM Sep 8 7:44 PM 6
7 Sep 8 8:07 PM Sep 8 8:28 PM 7
8 Study for Quiz On line and textbook help references: p involving parallel lines worked examples/v/ca geometry more proofs Sep 8 8:47 PM 8
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0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.
0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,
Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?
Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F
9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.
3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem
0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
Chapter 6 Summary 6.1. Using the Hypotenuse-Leg (HL) Congruence Theorem. Example
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Content Standards G.CO.10 Prove theorems about triangles. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to
Content Standards G.CO.10 Prove theorems about triangles. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working
Common Core Math 3. Can you find the error in this proof. Unit 2B - Proofs
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Chapter 2. Reasoning and Proof
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Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg ( )
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