G7-3 Measuring and Drawing ngles and Triangles right angle acute angles obtuse angles 90 less than 90 more than 90 and less than 180 1. Without using a protractor, identify each angle as acute or obtuse. a) b) c) d) 2. Practise choosing the correct scale to measure an angle. Step 1: Is the angle acute or obtuse? ircle your answer. Step 2: ircle the 2 numbers that the arm of the angle passes through. Step 3: hoose the correct angle measure. Example: if the angle is acute, the measure is less than 90. a) b) The angle is acute / obtuse. The angle is acute / obtuse. The angle measures. The angle measures. c) d) The angle is acute / obtuse. The angle is acute / obtuse. The angle measures. The angle measures. 102 Geometry 7-3 OPYRIGHT 2009 JUMP MTH: NOT TO E OPIED
3. Measure each angle. Hint: For parts d) and e), you will have to extend the arms. a) b) c) d) e) 4. In each polygon, circle angle ÐXYZ. Then measure the angle. a) b) c) X Y Y U V X Z Z W W Z W V Y X Measure of ÐXYZ : Measure ofðxyz : Measure of ÐXYZ : 5. Ð is 90. ÐD is 50. D OPYRIGHT 2009 JUMP MTH: NOT TO E OPIED 50 a) What is the measure of ÐD? How do you know? b) Measure ÐD with a protractor to check your answer in a). Geometry 7-3 103
G7-4 Perpendicular Lines Perpendicular lines meet at a right angle (90 ). The ^ symbol means is perpendicular to. EG ^ ZF ^ ST Z S E F G T 1. Name the perpendicular lines. a) b) K c) d) D S P E J F D T Q E ^ ^ ^ ^ 2. re the pairs of lines below perpendicular? Measure the angle where they meet to check. Draw a square corner ( ) to show any perpendicular lines. a) b) c) d) e) 3. Match the diagrams to the descriptions. OPYRIGHT 2009 JUMP MTH: NOT TO E OPIED.. P point P on line segment lines perpendicular to P. D. P P lines that pass through point P on the line perpendicular to that passes through point P Geometry 7-4 105
^ ^ ^ ^
G7-6 Parallel Lines Parallel lines never intersect, no matter how far they are extended in either direction. 1. Extend both lines. Use a ruler. Do the lines intersect or are they parallel? 2. Match the descriptions to the lines.. The lines intersect.. If the lines were extended far enough, they would intersect.. The lines are parallel. 3. Give two examples of parallel lines in the world around you. We mark parallel lines using an equal number of arrow symbols (>, >>, and so on). The symbol means is parallel to. Example: D. D 4. Use arrow symbols to mark the sides or edges of these shapes that look like they are parallel. a) b) c) d) OPYRIGHT 2009 JUMP MTH: NOT TO E OPIED 5. State which lines are parallel. F R a) b) c) X T U L Y G S G E F M H Geometry 7-6 109
Determining If Two Lines re Parallel If two lines are perpendicular to another line, then they are parallel. If two lines are parallel, any line perpendicular to one of the parallel lines will be perpendicular to the other. 6. Mark any parallel lines. State which lines are parallel. U N O D a) b) c) d) M E F R L W X S V K V H Y J EF 7. omplete the statements. K Q a) is parallel to and KL is perpendicular to D, so KL is also perpendicular to. R D b) and QR ^, so,qr ^. L 8. a) ll the angles in a rectangle are right angles. Mark the right angles on this rectangle. b) D ^ and D ^, so D ^ D and D ^, so D c) Explain how you know that these pairs of sides are parallel. D 9. ircle the flags that contain parallel lines (not counting the edges of the flags). OPYRIGHT 2009 JUMP MTH: NOT TO E OPIED 110 Geometry 7-6
G7-7 ngle Relationships shared arm shared vertex straight angle adjacent angles linear pair straight angle measures 180. djacent angles Ð a and Ð b The sum of the angles have a shared vertex and arm. in a linear pair is 180. a b a b 1. Match the diagrams to the names. Hint: The angles in a linear pair are also adjacent angles. straight angle: adjacent angles: linear pair:... a b b a a b 2. alculate these angle sums. a) 10 + 25 = b) 30 + 40 = c) 12 + 28 = d) 20 + 30 + 40 = 3. Ð1 and Ð2 are a linear pair. Identify the three other linear pairs in the diagram. Ð and Ð Ð and Ð Ð and Ð 1 4 2 3 4. Determine the sum of the angles formed by two lines that intersect at a right angle. 1+ 2 = 90 + 90 = 3 + 4 = 90 + 90 = So, 1+ 2 + 3 + 4 + = 1 3 2 4 5. Determine the sum of the angles formed by any two intersecting lines. The sum of the angles in a linear pair is. So, 1+ 2 = and 3 + 4 = So, 1+ 2 + 3 + 4 = 4 3 1 2 6. Predict the sum of the four angles around any point P. alculate these angle sums to check your prediction. 150 95 85 30 30 85 150 95 30 + 150 + 30 + 150 = 95 + 85 + 95 + 85 = OPYRIGHT 2009 JUMP MTH: NOT TO E OPIED 112 Geometry 7-7
XZY XZY = + + = 180 = 180 ( 80 + 30 ) = 180 = F