1 / 12

coordinate proof

5.8 Vocabulary. coordinate proof. Coordinate proofs use coordinate geometry to prove geometric relationships or properties for figures.

eringarrett
Télécharger la présentation

coordinate proof

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5.8 Vocabulary coordinate proof Coordinate proofs use coordinate geometry to prove geometric relationships or properties for figures. General Case: proves properties/relationships of figures which are specified in terms of variables: any square, any rectangle, any rhombus, etc. Properties will always be true Specific Case: proves properties/relationships for figures given by actual coordinates. Properties are only certain for that case.

  2. General: To prove the general case you assign variables as the coordinates of the figure. If a coordinate proof requires calculations with fractions, choose coordinates that make the calculations simpler. For example, use multiples of two when you are to find coordinates of a midpoint (2a, 2b, etc.)

  3. Positioning Shapes

  4. Once the figure is placed in the coordinate plane, you can use Slope, Distance, or the Midpoint Formulas to prove statements about the figure. Slope: m = MidPoint: M = Distance: d =

  5. Example 1A: Assigning Coordinates to Vertices Position each figure in the coordinate plane and give the coordinates of each vertex. rectangle with length twice the width

  6. Example 1B: Assigning Coordinates to Vertices Position each figure in the coordinate plane and give the coordinates of each vertex. A right triangle with legs of lengths s and t Position a square with side length 4p in the coordinate plane and give the coordinates of each vertex.

  7. Example 2: Specific Figures in the Coordinate Plane Position a square with a side length of 6 units in the coordinate plane. You can put one corner of the square at the origin. Position a right triangle with leg lengths of 2 and 4 units in the coordinate plane. (Hint: Use the origin as the vertex of the right angle.)

  8. Example 3: Specific Coordinate Proof Given: D(–4, 4), E(–2, 1), F(–6, 1), G(3, 1), H(5, –2), J(1, –2). Prove: ∆DEF  ∆GHJ

  9. Example 4: Using CPCTC In the Coordinate Plane Given:D(–5, –5), E(–3, –1), F(–2, –3), G(–2, 1), H(0, 5), and I(1, 3) Prove:DEF  GHI

  10. Example 4: General Coordinate Proof Given: Rectangle PQRS Prove: The diagonals are 

  11. Lesson Quiz: Part I Position each figure in the coordinate plane. 1. rectangle with a length of 6 units and a width of 3 units 2. square with side lengths of 5a units

  12. 3. Given: Rectangle ABCD A(0, 0), B(0, 8), C(5, 8), and D(5, 0). E is mdpt. of BC, F is mdpt. of AD. Prove: EF = AB 4. Honors: Show that if a segment is drawn from the vertex of the right angle to the midpoint of the hypotenuse it divides the triangle into two triangles which each have an area equal to half the area of the right triangle. Lesson Quiz: Part II

More Related