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Common Core State Standards for Mathematical Content Congruence G-CO

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Common Core State Standards for Mathematical Content Congruence G-CO

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  1. Unit 1.3 - Segment and angle relationships1.3a Prove theorems involving the Segment Addition Postulate1.3b Formal geometric constructions using a variety of tools and methods to copy and bisect an angle1.3c Prove theorems involving the Angle addition postulate 1.3d Prove theorems about angle pairs 1.3e Prove theorems involving parallel lines and transversals1.3f Formal geometric constructions using a variety of tools and methods to construct perpendicular lines. Common Core State Standards for Mathematical Content Congruence G-CO Prove geometric theorems [Focus on validity of underlying reasoning while using variety of ways of writing proofs] 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. G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

  2. 1.3a Prove theorems involving the Segment Addition Postulate Postulate: Mathematical statement that is accepted without proof

  3. Let B be between A and C 1 -3 6 Find: AB = 4 AC = 4 + 5 = 9 BC= 5 AC= 9 Write an equation for AC in terms of AB and BC AC = AB + BC

  4. Segment Addition Postulate • If B is between A and C, then AB + BC = AC. C B A

  5. Write a mathematic equation for FA using the segment addition postulate. What would the equation look like now? FA =

  6. If N is between M and P and MN = 10, MP = 25, find NP 25 10

  7. A flight from PVD to NYC is 143 miles A flight from PVD to Washington DC is 355 miles A flight from NY to Washington DC is _____ miles

  8. Seg. Add. Post. Example • If J is between H and K and HJ=5x-3 , JK = 4x, HK = 8x, find HJ, JK, HK • Ans: Draw a diagram

  9. Example • M is between L and N. Find each measurement if: LM = 4x+6 , LN = 5x+10 MN = 3x – 4 LM + MN = LN LM =4(4)+6 = 22 MN = 3(4)-4 = 8 LN = 5(4)+10 = 30

  10. If U is between T and B, find the value of x and the measure of if TU= 4x – 1, UB = 2x -1, and TB = 5x Explain all your work

  11. Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F G FG=2 DF=7 DG=9 EG=7

  12. Write an expression for QR 13x + 25 8x+5 PR = PQ + QR 13x + 25 = (8x+5) + QR -8x -8x 5x + 25 = 5 + QR -5 -5 5x + 20 = QR QR =5x + 20

  13. Segment bisectors M is the midpoint of and AM = MB Segment AM is CONGRUENT to segment MB Congruent segments: Segments that have the same length

  14. M is the midpoint of . Find AM and MB 26

  15. P is the midpoint of Find PS and RS. 7

  16. If M is the midpoint of , AM = 2x + 11, MB = 4x – 5 Find the value of x and the measure of 2x + 11 4x - 5

  17. CP GeometryAssignment In class assignment: Practice worksheet 1.3a Segment addition postulate & midpoint theorem Homework : Page 33: 22-25, 38-40, Page 41: 15-23, 33-35

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