BELLWORK Find the midpoint between the following pairs of points.

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Presentation transcript:

BELLWORK Find the midpoint between the following pairs of points. (0,0) and (10,6) 2. (-2,7) and (4,-1) 3. (a,0) and (0,b) Find the distance between the following pairs of points. 4. (0,0) and (3,-4) 5. (-2,-1) and (4,7) 6. (a,2b) and (0,2b) Find the slope between the following pairs of points. 7. (0,0) and (3,-4) 8. (-2,-1) and (4,7) 9. (a,2b) and (0,2b)

Unit 4 – Triangle Congruence 4.8 Coordinate Proof A coordinate proof is a style of proof that uses coordinate geometry and algebra. The first step of a coordinate proof is to position the given figure in the plane. You can use any position, but some strategies can make the steps of the proof simple. There is no firm rule but experience will help in deciding with strategy to use. 1. Use the origin as a vertex and keep the figure in Quad I. 2. Center the figure at the origin. 3. Center a side at the origin. 4. Use the axes as the side of the figure.

Unit 4 – Triangle Congruence 4.8 Coordinate Proof Once the figure is placed in the coordinate plane, you can use slope, the coordinates of the vertices, the Distance Formula, or the Midpoint Formula to prove statements about the figure. Hint: If you think you’ll use midpoint use coordinates in multiples of 2.

Show: The diagonals of a rectangle are congruent. Unit 4 – Triangle Congruence 4.8 Coordinate Proof Show: The diagonals of a rectangle are congruent.

Show: The diagonals of a rectangle bisect each other. Unit 4 – Triangle Congruence 4.8 Coordinate Proof Show: The diagonals of a rectangle bisect each other.

Unit 4 – Triangle Congruence 4.8 Coordinate Proof Show: The midpoints of the sides of rectangle form a figure whose both pairs of opposite sides are parallel.

Unit 4 – Triangle Congruence 4.8 Coordinate Proof Show: that the midsegment of a triangle is parallel to the third side and half the length. (note: the midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle.

Homework: Prove that the diagonals of a square are perpendicular. Unit 4 – Triangle Congruence 4.8 Coordinate Proof Homework: Prove that the diagonals of a square are perpendicular. Prove that the midpoints of the sides of a square form a square (hint: show all sides congruent and adjacent sides are perpendicular). Prove that the midsegment of a triangle is parallel to the third side and half the length. (note: the midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle.