Quadrilaterals and Coordinates Proof Properties of rectangles, rhombus and squares Opening routine Find x and y if the quadrilateral is a parallelogram

Topic IV: Quadrilaterals and Coordinate Proof

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares Objective: Use congruency between triangles to prove that a quadrilateral is rectangle. Essential Question: What properties can be used to determine if a quadrilateral is a rectangle?

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares Vocabulary Parallelogram: Is a quadrilateral with two pairs of parallel sides. Rectangle: Is a quadrilateral with four right angles. Rhombus: Is a simple quadrilateral whose four sides all have the same length. Square: A square is a regular quadrilateral, which means that it has four equal sides and four equal angles.

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares Vocabulary Trapezoid: Is a quadrilateral that has a pair of opposite sides parallel. The sides that are parallel are called “bases”. Isosceles trapezoid: Is a special type of trapezoid in which non-parallel sides and base angles are equal. Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares Use the properties of the rectangles to find the measures of 1 and 2. As the triangles form by the diagonal MP are right triangles, then: (3x)o + (2x + 20)o + 90o = 180o 3x + 2x + 20 = 90o 5x = 70o x = 14o As 1 and QMP are complementary, 1 + QMP = 90o 1 + 3x = 90o 1 + 3(14) = 90o 1 + 42o = 90o 1 = 48o As 2 and QMP are alternate interior angles, then 2 = 42o.

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares Guided Practice – WE DO Points ABCD are midpoints of the sides of the larger square. If the larger square has area 60, what's the small square's area? A) 20 B) 25 C) 30 D) 45

Quadrilaterals and Coordinates Proof Properties of rectangles, rhombi and squares Independent Practice - YOU DO Worksheet “Properties of rectangles, rhombi and squares” Exercises from 1 to 24

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Closure Essential Question: What criteria can be used in a coordinate proof to determine of a quadrilateral is a parallelogram?