Quadrilaterals and Coordinates Proof Review Topic IV Opening routine

Topic IV: Quadrilaterals and Coordinate Proof

Quadrilaterals and Coordinates Proof Review Topic IV Objective: Use properties of parallelograms, rectangles, rhombi and squares to solve problems. Essential Question: How the slope criteria for parallel lines can be used to determine if a quadrilateral is a parallelogram?

Quadrilaterals and Coordinates Proof Review Topic IV 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 Review Topic IV Vocabulary Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. Trapezoid: Is a quadrilateral with exactly one pair of parallel sides. Base of a trapezoid: The parallel sides of a trapezoid are called bases. Leg of a trapezoid: The non-parallel sides of trapezoid are called legs.

Quadrilaterals and Coordinates Proof Review Topic IV Vocabulary Base angle of a trapezoid: The base angles are formed by a base and one of the legs. Isosceles trapezoid: Is a special type of trapezoid in which non-parallel sides and base angles are equal. Midsegment of a trapezoid: Is the segment whose endpoints are the midpoints of the legs. The midsegment is parallel to each base.

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV Coordinates Proof for Parallelograms To prove if a quadrilateral in the coordinate plane is a parallelogram, it can be used four different criteria: Distance formula to determine if both opposite sides are congruent. Slope formula to determine if both opposite sides are parallel. Midpoint formula to determine if the diagonals bisect each other. Distance formula and slope formula to determine if one pair of opposite sides is both parallel and congruent.

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV Test for Rectangle in the Coordinate Plane To prove if a quadrilateral in the coordinate plane is a rectangle, first proof the quadrilateral is a parallelogram, then it can be used two different methods: Method 1: Show that the diagonals are congruent. Method 2: Show that it has a right angle by using slope.

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV Test for Rhombus in the Coordinate Plane To prove if a quadrilateral in the coordinate plane is a rhombus, first proof the quadrilateral is a parallelogram, then it can be used two different methods: Method 1: Prove that the diagonals are perpendicular. Method 2: Prove that a pair of adjacent sides are equal. Method 3: Prove that all four sides are equal.

Quadrilaterals and Coordinates Proof Review Topic IV Conditions for squares The conditions for squares are a combination of the conditions for rectangles and rhombi. 1. If one angle is a right angle 2. If the diagonals are congruent 3. If one pair of consecutive sides The are congruent. parallelogram 4. If the diagonals are perpendicular. is a square 5. If one diagonal bisect a pair of opposite angles

Quadrilaterals and Coordinates Proof Review Topic IV Test for Squares in the Coordinate Plane To prove if a quadrilateral in the coordinate plane is a square, there are many ways to do this : I recommend proving that: 1. Diagonals bisect each other (parallelogram). 2. Diagonals are congruent (only rectangles and squares). 3. Diagonals are perpendicular (only squares).

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV

Quadrilaterals and Coordinates Proof Review Topic IV .

Quadrilaterals and Coordinates Proof Review Topic IV Independent Practice - YOU DO Worksheet “Review Topic IV” Questions 16 – 25

Quadrilaterals and Coordinates Proof Review Topic IV Closure Essential Question: How the slope criteria for parallel lines can be used to determine if a quadrilateral is a parallelogram?