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Geometry

Geometry. Lesson 4 – 8 Triangles and Coordinate Proof. Objective: Position and label triangles for use in coordinate proofs. Write coordinate proofs. Coordinate Proof. Coordinate proof – use figures in the coordinate plane and algebra to prove geometric concepts. Key Concept.

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Geometry

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  1. Geometry Lesson 4 – 8 Triangles and Coordinate Proof Objective: Position and label triangles for use in coordinate proofs. Write coordinate proofs.

  2. Coordinate Proof • Coordinate proof – use figures in the coordinate plane and algebra to prove geometric concepts.

  3. Key Concept • Use the origin as a vertex or center of the triangle. • Place at least one side of a triangle on an axis. • Keep the triangle within the first quadrant if possible. • Use coordinates that make computations as simple as possible.

  4. Position and label right triangle MNP on the coordinate plane so that leg MN is a units long and leg NP is b units long.

  5. Position and label isosceles triangle JKL on the coordinate plane so that its base JL is a units long, vertex K is on the y-axis, and the height of the triangle is b units.

  6. Identify Missing Coordinates of isosceles triangle XYZ Z (a, 0) X (0, 0)

  7. Name the missing coordinates of isosceles right triangle ABC. A (0, a) C (a, 0) B (0, 0)

  8. Write a coordinate proof to show that a line segment joining the midpoints of two sides of a triangle is parallel to the third side. Sketch a picture. Use numbers that will make the problem easier. Midpoint deals with dividing by 2 so use multiples of 2 to make it simple. Cont…

  9. Proof Using Midpoint formula: Using Slope formula: Since the slopes are equal,

  10. The Bermuda Triangle is a region formed by Miami, Florida, San Jose, Puerto Rico, and Bermuda. The approximate coordinates are given. Write a coordinate proof to prove the Bermuda triangle is scalene. Since all sides are different, Triangle MBP is scalene.

  11. Homework • Pg. 304 1 – 4 all, 8 – 18 E, 32, 38 – 46 E

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