1. Continuation of MVP 8.3 PROVE IT!

2. STANDARD:
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle.

3. I will . . .
use slopes and distance to show that particular quadrilaterals are parallelograms, rectangles, rhombi or squares.

4. EQ:
How do I use Algebra to show that a quadrilateral is a Parallelogram, a Rectangle, a Rhombus, or a Square?

5. WARM UP: How do you know a quadrilateral is a Rectangle?
How do you know a quadrilateral is a Rhombus?
How do you know a quadrilateral is a Square?

6. Properties of a . . .
Parallelogram: opposite sides are parallel. USE: SLOPE FORMULA RECTANGLE:  Show that it has four right angles. USE SLOPE FORMULA  Show that it is a parallelogram with diagonals that are congruent. USE DISTANCE FORMULA RHOMBUS:  Show that it has four congruent sides (Definition of Rhombus) SQUARE: If a quadrilateral has four congruent sides and four right angles, then it’s a square.

7. WHAT DO YOU USE TO SHOW THIS?
A Rectangle has:
I can prove a quadrilateral is a Rectangle by . . .
Showing that the diagonals are congruent AND
Showing there are 4 right angles.
WHAT DO YOU USE TO SHOW THIS?

8. Right Triangles

9. How can you prove a triangle is a Right Triangle?
First Way:
FACT: Pythagorean Theorem ONLY works for a RIGHT Triangle.
FACT: Find the length of the sides by using the Distance Formula.
Second Way:
FACT: A Right triangle has ONE 90° angle.
FACT: Find the SLOPES of 2 sides and see if they are OPPOSITE RECIPROCALS.