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BLM Measuring and Drawing Angles and Triangles Measuring an Angle

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BLM Measuring and Drawing Angles and Triangles Measuring an Angle BLM Measuring and Drawing Angles and Triangles Measuring an angle 30° 0° arm origin base line 0° 180° If the arms are too X Place the origin Y Rotate the protractor Z Look at that arm [ Use that scale to short to reach the of the protractor so the base line is of the angle and find the protractor scale, over the vertex of exactly along one of the choose the scale measurement. lengthen them. the angle. arms of the angle. that starts at 0°. Drawing an angle angle angle mark mark 60° X Draw a line Y Place the protractor with the Z Hold the protractor in place [ Draw a line from the segment. origin on one endpoint. This point and mark a point at the angle vertex through the will be the vertex of the angle. measure you want. angle mark. Drawing lines that intersect at an angle 45° 45° P P P X Draw a line. Mark a point P on Y Draw an angle of the given Z Extend the arms of your angle to the line. measure using P as vertex. form lines. Drawing a triangle 90° 30° 90° 90° 30° 90° 30° 5 cm 5 cm 5 cm 5 cm X Sketch the Y Use a ruler to Z & [ Use a protractor to draw the angles \ Erase any extra triangle you want draw one side of the at each end of this side. Extend the arms arm lengths. to draw. triangle. until they intersect. BLM Drawing Perpendicular Lines and Bisectors Drawing a line segment perpendicular to AB through point P Using a set square P P A P B A P B A B A B Here point P is on AB. Here point P is outside AB. Using a protractor P P A P B A B A P B A B Here point P is on AB. Here point P is outside AB. Drawing the perpendicular bisector of line segment AB M A B A B A B M M A B M X Use a ruler to determine Y Use a set square or a protractor to draw The line you have drawn the midpoint of the line a line perpendicular to AB that passes is the perpendicular segment. Label it M. through M. bisector of AB. BLM Drawing Parallel Lines Drawing a line parallel to AB through point P Using a set square P P P P A B A B A B A B X Line up one of the Y Use the set square Z Draw a line [ Erase the line you short sides of the set and a straightedge to perpendicular to the no longer need. square with AB. draw a perpendicular to new line that passes AB. through P. Using a protractor P P P P A B A BA B A B X Line up the 90° line on the protractor with AB. Y Line up the 90° line on the protractor with the Use the straight side of the protractor to draw a line line segment drawn in step 1, and the straight side segment perpendicular to AB. of the protractor with point P. Draw a line parallel to AB. Erase the first perpendicular you drew. BLM Properties of Parallel Lines Investigation What happens if two lines meet a third line at the same angle, but it is not a right angle? A. Draw a pair of parallel lines and a third line intersecting both at an angle that is not a right angle. Measure all the angles you see. What do you notice? E B. ∠ABD = ∠ACE = 70°. Draw a perpendicular to BD through D C point A. Extend it to meet CE. Is the line you drew perpendicular to CE? Check using a protractor. What can you say about the lines BD and CE? B A D C. ∠ABD = ∠ACE = 70°. Are the lines BD and CE parallel? E B A 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. C E. Compare the pattern between the equal angles ∠ABD and C E E ∠ACE in parts B and D. Which one looks more like the angles B D A marked in the letter C and which one is more like angles in the D letter F? A B 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. BLM Distance Between Parallel Lines 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. B. 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 B are parallel. D. A parallelogram is a 4-sided polygon with opposite sides parallel. You can draw parallelograms by using anything with parallel sides, like a ruler. Place 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? BLM Sum of the Angles in a Triangle (1) Investigation What is the sum of the angles in a triangle? A. 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 _____°. B. List the sum of the measures of the angles in each triangle. 70° 20° 56° 56° 90° 68° _____° + _____° + _____° = _____° _____° + _____° + _____° = _____° 39° 25° 25° 116° 25° 130° _____° + _____° + _____° = _____° _____° + _____° + _____° = _____° 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 _____°. BLM Sum of the Angles in a Triangle (2) C. Calculate the sum of the angles. 70° 92° 55° 55° 70° 18 ° ____° + ____° + ____° = ____° ____° + ____° + ____° = ____° 24° 25° 130° 132° 26° 23° ____° + ____° + ____° = ____° ____° + ____° + ____° = ____° What do you notice about the sums of the angles? _________________________________ D. Cut out a paper triangle and fold it as follows: X Find the midpoints of the Y Fold the triangle along the Z Fold the other two vertices sides adjacent to the largest new line so that the top vertex of the triangle so that they angle (measure or fold). Draw a meets the base of the triangle. meet the top vertex. line between the midpoints. You will get a trapezoid. The three vertices folded together add up to a straight angle. What is the sum of the angles in a straight angle? _____° So ∠A + ∠B + ∠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 B? Explain. F. In fact, it has been mathematically proven that… The sum of the angles in a triangle is ______°. BLM 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. 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 BLM Protractors BLM Circles BLM Quadrilaterals BLM Quadrilaterals BLM Regular Polygons .
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