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Teacher’s Guide Geometer’s Sketchpad Classifying Quadrilaterals Student Worksheet Assignment 1 Constructing Quadrilaterals Directions: This worksheet will guide you through the Classifying Quadrilaterals assignment. Questions should be answered in the space provided. Sketches should be made in a new file in Geometer’s Sketchpad. Both the file and this worksheet will be graded. Be sure to save often to be sure not to lose any of your work. Open Geometer’s Sketchpad and choose File new sketch. Go to the File menu and choose Save As and save the file as Quad1 followed by your first initial and last name. (For example, I would save my file as quad1 R Grunloh.gsp) As you work through the constructions below, create a text box next to each shape to name the type of quadrilateral you created. 1. Construct a quadrilateral. Drag the vertices of the quadrilaterals. Can you make this quadrilateral into a parallelogram?__Yes_ A square?__Yes__ Is this quadrilateral always a parallelogram?___No___ Always a square?__No__ In the space below, briefly explain the why or why not? Answers will vary. Points may be moved to create different quadrilaterals but if you want the sides to always be perpendicular then they must be constructed using perpendicular lines. 2. Construct a parallelogram. Think about the properties that make a quadrilateral a parallelogram. Your construction should always maintain its parallelogram properties. In the space below, explain how you guaranteed that your construction would always be a parallelogram. Construct a segment (AB) Construct a point (C) not on the segment Construct a line parallel to the side AB and through the point C Construct side AC Construct a line parallel to AC through the point B Construct the intersection of the parallel lines, point D Construct the segments CD and BD Hide the parallel lines A B C D 1 Teacher’s Guide 3. Construct a Rectangle. Think about the properties that make a quadrilateral a rectangle. Your construction should always maintain the properties of a rectangle. In the space below, explain how you guaranteed that your construction would always be a rectangle. Construct a segment (EF) Construct a line perpendicular to EF through point E Construct a point on the perpendicular line (G) Construct a line perpendicular to EF through point F Construct perpendicular to the line EG Construct the intersection (H) of the last two lines constructed Construct the segments EG, GH, and FH Hide the perpendicular lines E F G H 4. Construct a Rhombus. Think about the properties that make a quadrilateral a rhombus. Your construction should always maintain the properties of a rhombus. In the space below, explain how you guaranteed that your construction would always be a rhombus. Construct a segment (JK) Construct a circle with center J and point K on the circle Construct point L on the circle Construct segment JL Construct a line parallel to JK through point L Construct a line parallel to JL through point K Construct the intersection (M) of the new parallel lines Construct segments JL, LM, and KM Hide the circle and the parallel lines J K L M 2 Teacher’s Guide 5. Construct a Square. Think about the properties that make a quadrilateral a square. Your construction should always maintain the properties of a square. In the space below, explain how you guaranteed that your construction would always be a square. Construct a segment (NO) Select segment NO and point O and mark point N as the center of rotation (double click on N or select N and choose Transform-Mark Center) Rotate 90 degrees (O’) Construct a line perpendicular to O’N through point O’ Construct a line perpendicular to ON through point O Construct the intersection of the two new perpendicular lines (P) Construct segments O’P and OP Hide the perpendicular lines O' P N O 6. Construct a Trapezoid. Think about the properties that make a quadrilateral a trapezoid. Your construction should always maintain the properties of a trapezoid. In the space below, explain how you guaranteed that your construction would always be a trapezoid. Construct a segment (QR) and a point not on the segment (S) Construct a line parallel to QR through the point S Construct a point (T) on this new line Construct the three missing sides Hide the parallel line Q R S T 3 Teacher’s Guide 7. Construct an Isosceles Trapezoid. Think about the properties that make a quadrilateral an isosceles trapezoid. Your construction should always maintain the properties of an isosceles trapezoid. In the space below, explain how you guaranteed that your construction would always be an isosceles trapezoid. Construct a segment (WX) and a point not on the segment (Y) Construct a line parallel to WX through the point Y Construct the segment WY Construct the midpoint (U) of WX Construct a line perpendicular to WX through the midpoint U Select the segment WY and the endpoints W and Y Mark the perpendicular line as the mirror Transform-Reflect Construct the segment YY’ Hide the parallel line, perpendicular line, and the midpoint U W X Y Y' 4 Teacher’s Guide Geometer’s Sketchpad Classifying Quadrilaterals Assignment 2 Identifying Quadrilaterals Open your file created in Assignment one. Choose File/Save As/ and save the file as quad2 followed by your first initial and last name. Using your selection tool (the arrow), highlight a box around your entire sketch. Choose Display/Hide Labels Using the Test Tool, click on the bottom side of each quadrilateral. This will create a label for the bottom side. Double click on this label and change the label to read QUAD and a number 1-7 (Number these in some random order). At the bottom of this sheet, write the label in your file that corresponds to each shape. Delete all text boxes that label your quadrilaterals (rectangle, square, etc) Using the selection tool, drag the vertices of each quadrilateral so that each quadrilateral appears to be a square. Move the quadrilaterals so that they are in numerical order. (The easiest way to move the quadrilaterals would be to use the selection tool and select all points and segments in the quadrilateral and then drag the quadrilateral.) Save your file. Complete the Student Worksheet for assignment 2 and turn it in along with this page. My File Name is _QUAD2 R Grunloh.gsp________________ My quadrilaterals are labeled as: My Quadrilateral is QUAD_3_ My Parallelogram is QUAD_2_ My Rectangle is QUAD_6_ My Rhombus is QUAD_7_ My Square is QUAD_1_ My Trapezoid is QUAD_5_ My Isosceles Trapezoid is QUAD_4_ 5 Teacher’s Guide Geometer’s Sketchpad Classifying Quadrilaterals Student Worksheet Assignment 2 Directions: Open three of your classmates files and determine the more specific names of their quadrilaterals and answer the questions below. File Name: File Name: File Name: Quadrilateral Answers will Vary Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Based on your observations in both Assignment one and Assignment two, describe the properties that helped you identify the following shapes. Answers will vary Parallelogram Opposite sides are always parallel but not always congruent. Angles are not always right angles. Rectangle Opposite sides are always parallel and adjacent sides are always perpendicular (or make right angles). All sides are not always congruent Rhombus Opposite sides are always parallel and all sides are congruent. Angles are not always right angles Square Opposite sides are always parallel and adjacent sides are always perpendicular (for right angles). All sides are always congruent. Trapezoid Only one set of sides are always parallel (**Worth noting – by definition a trapezoid may not be a parallelogram although this sketch allows that) Isosceles Trapezoid Only one set of sides are always parallel (**Worth noting – by definition a trapezoid may not be a parallelogram although this sketch allows that) The nonparallel sides are always congruent 6 Teacher’s Guide Geometer’s Sketchpad Classifying Quadrilaterals Student Worksheet Assignment 3 Quadrilaterals Properties Open your original quadrilateral file Resave the file as Quad3 followed by your first initial and last name. Construct the diagonals of the different quadrilaterals. Experiment with the different quadrilaterals and complete the chart below. Measure segments and angles to help you. But an X in each box that is true for each quadrilateral. Save your file with the calculations and measurements displayed. Isosceles Parallelogram Rectangle Rhombus Square Trapezoid Trapezoid Both Sets of Opposite Sides X X X X are Parallel Only One Set of Opposite Sides X X are Parallel Opposite Sides Non are Congruent Parallel X X X X Sides are Congruent All Sides are Congruent X X Opposite Angles are Congruent X X X X Adjacent Angles X are This is true Supplementary X X X X X vertically but not horizontally All Angles are Congruent X X (Right Angles) Base Angles are Congruent X Diagonals are Congruent X X X Diagonals Bisect Each Other X X X X Diagonals Bisect the Angles X X Diagonals are Perpendicular X X 7 Teacher’s Guide 8

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posted: | 6/5/2010 |

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