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Coordinate Geometry: Shapes, Triangles, and Proofs

Learn about basic geometric shapes, types of triangles and quadrilaterals, slope, parallel and perpendicular lines, and formulas for area and perimeter. Explore coordinate geometry and develop proofs using coordinates. Discover theorems about circles, parallel lines, and midpoints.

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Coordinate Geometry: Shapes, Triangles, and Proofs

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  1. Unit 3 Ms. Branch

  2. Do Now • What do you think coordinate geometry is? Write a web.

  3. Overview Notes • What you should know? • Basic Geometric Shapes • Types of Triangles and Quadrilaterals • Slope • Parallel and Perpendicular Lines • Formula for computing area and perimeter (i.e. triangles and rectangles) • What you will learn? • Using coordinates and equations on lines. • Understanding distance and midpoints using coordinates. (i.e. formulas) • Polygonal shapes, triangles, and quadrilaterals in the coordinate plane. • Developing geometric proofs using coordinate geometry. • Circles

  4. Perimeter

  5. Preview Theorems • Parallel Lines Theorem • Perpendicular Lines Theorem • Triangle Midsegment Theorem • Midpoints of a Quadrilateral Theorem • Midpoints of Isosceles Trapezoid Theorem • Midpoint of the Hypotenuse of a Right Triangle Theorem • Diagonals of a Parallelogram Theorem

  6. Discussion • What animal exhibit do you think is halfway between the lion and the giraffe exhibit? What is the distance between the lion and the giraffe exhibit? Find the distance between the hippo and giraffe exhibits.

  7. Presentations • House map or Amusement Park Map blueprint • Locations you chose • How you found distance? • How you found midpoint? • What was your midpoint location? • Any other information you would like to share?

  8. Homework Link http://tinyurl.com/ptacso6 Due: Tomorrow

  9. Unit 3 Lesson 6: What Kind of Triangle? • Objective: Identify different types of triangles in a coordinate plane. • Slide 1: 1-4 check mark questions • Slide 3: Check mark questions: Use picture of triangles on grid • -Finding the distances and midpoint will help • Slide 4: Check mark question

  10. Writing Prompt • Reflection: • How was your learning experience today? • What parts did you understand? • What parts were confusing? • What can you tell me about slope on a coordinate plane?

  11. Do Now • Plot the points on a coordinate graph: • C (3, -5) • D (3, 4) • E (-2, -5) • Use the Distance Formula to find the distance from D to E. • Use the Pythagorean Theorem to find the distance from D to E.

  12. Quick Reflection: • What do you notice about finding the distance with both the Distance Formula and the Pythagorean Theorem? Are they different? Are they the same? Why? • What connection can you make with knowing about the hypotenuse of a triangle?

  13. Writing Prompt • What did you learn about Rene Descartes? • How is he an important mathematician? • What connection can Descartes make with coordinate geometry? • What else would you like to know about Descartes?

  14. Agenda • Unit 3 Lesson 5 • Unit 3 Lesson 6 (What Kind of Triangle?) • Gallery Problem: (Solving Word Problems Using Midpoints) • Gallery Problem: ( Coordinates of a Square) • File Name: Geoboard Activity

  15. Do Now – Happy Monday Word Bank -angles -sides Parallel -inverse -four -equal -right -perpendicular

  16. Do Now Your Assessment is found online on baxterhigh.org “Distance and Midpoint Quiz” Cohort B, Math Department Show work on a separate sheet of paper. *When submitted, come see Ms. Branch* At 7:55am, you will begin your distance and midpoint assessment. Until then: • Take out your notes to study • Ask any last minute questions. • Distribute iPads. • Lower your voices. • Focus

  17. What type of triangle? • (Scalene, Isosceles, Equilateral) • Finding coordinates that • make a square • -Find the center point of a circle -Finding the slope of a line - Parallel : Slopes of a parallel line has the same slope. -Perpendicular: Slopes of perp. Lines have a negative reciprocal -Area of an isosceles trapezoid (on a coordinate plane) - Perimeter of a parallelogram -Length of the radius of a circle -What makes two triangles similar? -Finding midpoint -Deciding if a circle goes through the origin TOPICS TO FOR UNIT 3 ASSESSMENT

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