Use properties of above shapes to solve problems Materials: Straightedge 2 sheets of Patty Paper Quadrilaterals To recognize and define parallelograms, rectangles, squares, rhombus, and trapezoids Use properties of above shapes to solve problems

Parallelogram Properties Use a ruler to draw two sets of intersecting parallel lines on your patty paper. Label the parallelogram ABCD. Place a second patty paper over the first and trace ABCD. Label the second parallelogram PQRS.

Continue Move the second patty paper over the first and compare side RS to side AB. How do the lengths of the opposite sides compare? Rotate and move the second patty paper over the first to compare opposite angles R and A or angles S and B. How do the opposite angles compare? Rotate the second patty paper around the first to compare<S and <A. What is their relationship? What can be drawn?

Quadrilaterals Essential Question: How to use the properties of quadrilaterals to find the missing measures?

Quadrilaterals Four-sided polygons Angles have the sum of 360 degrees

Polygon Closed figure Formed by segments Essentials: Nonessentials:

Parallelogram It’s a quadrilateral Two sets of parallel sides Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other

Rectangle Two sets of parallel sides Opposite sides are congruent All angles are congruent Diagonals are congruent and bisect each other It’s a parallelogram

Rhombus Two sets of parallel sides All sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals are perpendicular, bisect each other, and bisect the angles It’s a parallelogram

Square It’s a parallelogram, rectangle, and rhombus Two sets of parallel sides All sides are congruent All angles are congruent Diagonals are congruent, perpendicular, bisect each other, and bisect the angles

Trapezoid Exactly one pair of parallel sides Parallel sides are bases Nonparallel sides are legs If legs are congruent, then its an isosceles trapezoid Diagonals are congruent Median is a segment that joins the midpoints of its legs M= ½ (b1 + b2) It’s a quadrilateral.

Complete  8.2 Parallelograms  8.4 Rectangles, Rhombi, and Squares  (back) Quadrilaterals

Monday Warm-Up: find the missing measures Parallelogram Square 3 12 15 61 30 27 18

Practice Complete USE:  8.2 Parallelograms Quadrilateral Info Sheet  8.4 Rectangles, Rhombi, and Squares  (back) Quadrilaterals USE: Quadrilateral Info Sheet YOU MAY WORK WITH A PARTNER Quiz on Tuesday

Polygon Hierarchy Polygons Quadrilaterals Parallelograms Trapezoid Rectangles Rhombus Square

Polygon Hierarchy Due Date: Tuesday ~ Some classes of polygons are quadrilaterals, parallelograms, rectangles, trapezoids, rhombi, and squares. These classes are arranged in the hierarchy on next slide. Directions: Copy hierarchy. Explain in details (complete sentences) why the shapes are arranged as so. Use your yellow sheet, textbook, Geometry to Go, and/or internet as a reference. Be creative. You may write an explanation under each box, use poster board, etc. Find a real world picture for all seven shapes.  Due Date: Tuesday

Polygon Hierarchy Polygons Quadrilaterals Parallelograms Trapezoid Rectangles Rhombus Square

Tuesday Warm-Up: find the missing measures Square X = Rectangle X = (2x + 8)º (2x + 16) (4x + 6) 67

Practice Questions

Define quadrilateral. Answer: Four sided figure. Angle sum = 360ºº

Explain why a square is a rectangle, and why a rectangle is not considered as a square. Answer: A square always have 4 congruent sides where as a rectangles sometime have 4 congruent sides.

Properties of an isosceles trapezoid Answer: Congruent Legs Bases are parallel Base angles are congruent Diagonals are congruent

Parallelogram, rectangle, rhombus, or square? All angles are congruent. Answer: Rectangle and square

Parallelogram, rectangle, rhombus, or square? All sides are congruent. Answer: Rhombus and square

Parallelogram, rectangle, rhombus, or square? Diagonals are perpendicular. Answer: Rhombus and square

Parallelogram, rectangle, rhombus, or square? All sides and angles are congruent. Answer: square

QUIZ TIME ABSOLUTELY NO TALKING Work on your Polygon Hierarchy following quiz.

Monday Warm-Up: find the missing measures Rhombus Parallelogram 3 14 15 61 23 48 27 16

Trapezoid Draw an isosceles trapezoid ABCD Label the bases and legs What do know about the legs? Draw the diagonals What do know about the diagonals? Draw an isosceles trapezoid WXYZ Draw a median and label legs What is the formula to find the median B A D C W X Z Y

Isosceles Trapezoid If LK = 30, HJ = 42, Find RS. If RS = 17, HJ = 14, Find LK. H If RS = x + 5, (HJ + LK) = 4x + 6, Find RS. K L S R J

Isosceles Trapezoid 110 10 24 36

Practice: Quadrilaterals/Trapezoids Complete 8.1 and 8.5 Complete QuadPrac Quiz: Tuesday Project DUE Tuesday Test: Monday

ACTIVITY 1 ACTIVITY 2 Polygon Hierarchy QuadPrac All due TOMORROW! Explain why the shapes are arranged as is and attach a real world picture to each. Polygons ACTIVITY 2 Quadrilaterals Parallelograms Trapezoid QuadPrac Rhombus Critical Thinking Know the properties of each quadrilateral Find the missing measures Solve for x. Rectangles Square

Tuesday Warm-Up 3. X Y M N W Z 1. B A WXYZ is a trapezoid. M is the midpoint of XW and N is the midpoint of YZ. If WZ = 25 and MN = 18, find XY. If <Y is 123°, find <W. 4. Rectangle 1. B A C D Given ABCD, m< A = 3x + 4 and m< C = 5x – 28, find m< B. 2. Two adjacent angles of a parallelogram have measures (3x – 2) and (4x + 7). Find x. 36º 10

ACTIVITY ACTIVITY Polygon Hierarchy Quiz: Trapezoid Tuesday Agenda Project is due TODAY! Explain why the shapes are arranged as is and attach a real world picture to each. NO talking during quiz Do your BEST! Quiz: Trapezoid Polygons Quadrilaterals Parallelograms Trapezoid Tuesday Agenda Turn in Polygon Hierarchy √ QuadPrac Take Quiz: Trapezoids Complete Study Guide (Test Wednesday) Rhombus Rectangles Square

Wednesday List the properties of each shape without your yellow sheet. Parallelogram Rectangle Square Rhombus Isosceles Trapezoid

Chapter 6: Quadrilaterals Review…Review… Review Any questions from study guide? TEST….TEST…TEST Take your time! Do your BEST! SHOW all work for FULL credit. When finish, work on Dissections of Squares quietly. Need glue & scissors

Dissections of Squares ACTIVITY 1 Chapter 6 test TEST….TEST…TEST Take your time! Do your BEST! SHOW all work for FULL credit. When finish, work on Dissections of Squares quietly. Need glue & scissors ACTIVITY 2 Dissections of Squares Critical Thinking Cut out each figure (one at a time) and rearrange pieces to form a square. Glue pieces in the square provided.