Continuation of MVP 8.3 PROVE IT!

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.

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

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

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?

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.

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?

Right Triangles

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.