NME DTE Measuring and Drawing ngles and Triangles Measuring an angle 30 arm origin base line 0 180 0 If the arms are too short to reach the protractor scale, lengthen them. Step 1: lace the origin of the protractor over the vertex of the angle. Step 2: Rotate the protractor so the base line is exactly along one of the arms of the angle. Step 3: Look at that arm of the angle and choose the scale that starts at 0. Step 4: Use that scale to find the measurement. Drawing an angle angle mark angle mark 60 Step 1: Draw a line segment. Step 2: lace the protractor with the origin on one endpoint. This point will be the vertex of the angle. Step 3: Hold the protractor in place and mark a point at the angle measure you want. Step 4: Draw a line from the vertex through the angle mark. Drawing lines that intersect at an angle 45 45 Step 1: Draw a line. Mark a point on the line. Step 2: Draw an angle of the given measure using as vertex. Step 3: Extend the arms of your angle to form lines. Drawing a triangle 90 30 5 cm 5 cm Step 1: Sketch the triangle you want to draw. Step 2: Use a ruler to draw one side of the triangle. 90 5 cm 90 30 5 cm Step 3: Use a protractor to draw the angles at each end of this side. Extend the arms until they intersect. 90 30 5 cm Step 2: Erase any extra arm lengths. COYRIGHT 2010 JUM MTH: TO E COIED E-42 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE Drawing erpendicular Lines and isectors Drawing a line segment perpendicular to through point Using a set square Here point is on. Here point is outside. Using a protractor Here point is on. Here point is outside. Drawing the perpendicular bisector of line segment M M M M COYRIGHT 2010 JUM MTH: TO E COIED Step 1: Use a ruler to determine the midpoint of the line segment. Label it M. Step 2: Use a set square or a protractor to draw a line perpendicular to that passes through M. The line you have drawn is the perpendicular bisector of. lackline Master Geometry Teacher s Guide for Workbook 7.1 E-43
NME DTE Drawing arallel Lines Drawing a line parallel to through point Using a set square Step 1: Line up one of the short sides of the set square with. Step 2: Use the set square and a straight-edge to draw a perpendicular to. Step 3: Draw a line perpendicular to the new line that passes through. Step 4: Erase the line you no longer need. Using a protractor Step 1: Line up the 90 line on the protractor with. Use the straight side of the protractor to draw a line segment perpendicular to. Step 2: Line up the 90 line on the protractor with the line segment drawn in step 1, and the straight side of the protractor with point. Draw a line parallel to. Erase the first perpendicular you drew. COYRIGHT 2010 JUM MTH: TO E COIED E-44 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE roperties of arallel Lines Investigation What happens if two lines meet a third line at the same angle, but it is not a right angle?. Draw a pair of parallel lines and a third line intersecting both at an angle that is not a right angle.. D = CE = 70. Draw a perpendicular to D through point. Extend it to meet CE. Is the line you drew perpendicular to CE? Check using a protractor. What can you say about the lines D and CE? C E D C. D = CE = 70. re the lines D and CE parallel? D E C D. Draw a pair of lines that intersect at a 40 angle. Draw a third line that meets one of the lines at the same angle. Try to make the third line parallel to one of the lines you started with. Check by drawing a perpendicular. COYRIGHT 2010 JUM MTH: TO E COIED E. Compare the pattern between the equal angles D and CE in parts and D. Which one looks more like the angles marked in the letter C and which one is more like angles in the letter F? Mathematicians have proved that if two lines meet with a third line at the same angles creating a pattern like in the letter F, the lines are parallel. When the lines meet at a right angle, you do not have to worry about the pattern of equal angles they are all right angles. C D E C E D lackline Master Geometry Teacher s Guide for Workbook 7.1 E-45
NME DTE Distance etween arallel Lines InveStIgatIon Does the distance between parallel lines depend on where you measure it? a. Measure the line segments with endpoints on the two parallel lines with a ruler. Write the lengths of the line segments on the picture.. Use a square corner to draw at least three perpendiculars from one parallel line to the other, as shown. Measure the distance between the two parallel lines along the perpendiculars. What do you notice? C. Explain why all the perpendiculars you drew in part are parallel. D. parallelogram is a 4-sided polygon with opposite sides parallel. You can draw parallelograms by using anything with parallel sides, like a ruler. lace a ruler across both of the parallel lines and draw a line segment along each side of the ruler. Use this method to draw at least 3 parallelograms with different angles. e. Measure the line segments you drew between the two given parallel lines in part D. What do you notice? F. To measure the distance between two parallel lines, draw a line segment perpendicular to both lines and measure it. Does the distance between parallel lines depend on where you measure it? COYRIGHT 2010 JUM MTH: TO E COIED E-46 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE Sum of the ngles in a Triangle Investigation What is the sum of the angles in a triangle?. Circle the combinations of a 70 angle and another angle that will make a triangle. (Hint: Imagine the sides of the triangle extended will they ever intersect?) 70 80 70 90 70 100 70 110 70 120 Circle the combinations of a 50 angle and another angle that will make a triangle. 50 100 50 110 50 120 50 130 50 140 Circle the combinations of a 90 angle and another angle that will make a triangle. 90 70 90 80 90 90 90 100 90 110 Make a prediction: To make a triangle, the total measures of any two angles must be less than.. List the sum of the measures of the angles in each triangle. 70 20 57 55 90 68 + + = + + = 42 118 20 25 130 25 COYRIGHT 2010 JUM MTH: TO E COIED + + = + + = What do you notice about the sums of the angles? Do you think this result will be true for all triangles? Make a conjecture: The sum of the three angles in any triangle will always be. lackline Master Geometry Teacher s Guide for Workbook 7.1 E-47
NME DTE C. Calculate the sum of the angles. 70 90 68 20 57 55 + + = + + = 42 118 20 25 25 130 + + = + + = What do you notice about the sums of the angles? D. Cut out a paper triangle and fold it as follows: C C C Step 1: Find the midpoints of the sides adjacent to the largest angle (measure or fold). Draw a line between the midpoints. Step 2: Fold the triangle along the new line so that the top vertex meets the base of the triangle. You will get a trapezoid. Step 3: Fold the other two vertices of the triangle so that they meet the top vertex. The three vertices folded together add up to a straight angle. What is the sum of the angles in a straight angle? So + + C = e. Could you fold the vertices of any triangle along a line and get a straight angle as you did in part D? Do the results of the paper folding activity support your conjecture in part? Explain. F. In fact, it has been mathematically proven that the sum of the angles in a triangle is. COYRIGHT 2010 JUM MTH: TO E COIED E-48 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE Straw Quadrilaterals 1. Take 6 straws. Leave 2 straws whole. Cut 2 straws in half. Cut 2 straws into a quarter straw and a three-quarter straw. 2. Make as many quadrilaterals as you can with the combinations of 4 straws below. Try placing the straws at different angles. Try placing the straws in different orders. Sketch the quadrilaterals you make. a) 2 whole straws and 2 quarter straws b) 4 half straws c) 1 whole straw, 1 three-quarter straw, and 2 half straws d) 1 whole straw, 1 three-quarter straw, 1 half straw, and 1 quarter straw 3. Check off the correct ending for the statement. COYRIGHT 2010 JUM MTH: TO E COIED With any of the four given side lengths above, only one possible quadrilateral can be made exactly two different quadrilaterals can be made many different quadrilaterals can be made lackline Master Geometry Teacher s Guide for Workbook 7.1 E-49
NME DTE rotractors COYRIGHT 2010 JUM MTH: TO E COIED E-50 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE Circles COYRIGHT 2010 JUM MTH: TO E COIED lackline Master Geometry Teacher s Guide for Workbook 7.1 E-51
NME DTE Quadrilaterals (1) 1 2 3 4 5 6 COYRIGHT 2010 JUM MTH: TO E COIED E-52 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE Quadrilaterals (2) 7 8 9 10 11 12 COYRIGHT 2010 JUM MTH: TO E COIED lackline Master Geometry Teacher s Guide for Workbook 7.1 E-53
NME DTE 2-D Shapes Sorting Game (1) 13 14 More than one line of symmetry No lines of symmetry 15 16 No right angles Two or more right angles 17 18 Two or more acute angles Equilateral COYRIGHT 2010 JUM MTH: TO E COIED E-54 lackline Master Geometry Teacher s Guide for Workbook 7.1
NME DTE 2-D Shapes Sorting Game (2) 19 20 No obtuse angles Not equilateral 21 22 One or more acute angles t least one reflexive angle COYRIGHT 2010 JUM MTH: TO E COIED 23 24 t least two pairs of parallel sides ll angles equal lackline Master Geometry Teacher s Guide for Workbook 7.1 E-55
NME DTE Regular olygons COYRIGHT 2010 JUM MTH: TO E COIED E-56 lackline Master Geometry Teacher s Guide for Workbook 7.1