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G7-3 Measuring and Drawing Angles and Triangles right angle 90° acute angles obtuse angles 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. a) Step 2: Circle the 2 numbers that the arm of the angle passes through. Step 3: Choose the correct angle measure. Example: if the angle is acute, the measure is less than 90°. 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 °. °. COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED Step 1: Is the angle acute or obtuse? Circle your answer. °. Geometry 7-3 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) X b) Y Y X W Measure of ÐXYZ : Z COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED 5. ÐABC is 90°. ÐABD is 50°. U c) Z Z W V Measure of ÐXYZ : A V W Y X Measure of ÐXYZ : D 50˚ B a) What is the measure of ÐDBC ? C How do you know? b) Measure ÐDBC 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 AB ^ ST S Z E A G F B T 1. Name the perpendicular lines. a) b) K c) S P D A C AB B E D J E ^ C F B d) T ^ A Q ^ ^ 2. Are the pairs of lines below perpendicular? Measure the angle where they meet to check. Draw a square corner ( a) ) to show any perpendicular lines. b) c) d) e) COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED 3. Match the diagrams to the descriptions. A. B. A P B A C. P B A D. P B A B P point P on line segment AB lines that pass through point P on AB lines perpendicular to AB the line perpendicular to AB 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. A. The lines intersect. B. If the lines were extended far enough, they would intersect. C. 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.” B C Example: AB || CD. A D 4. Use arrow symbols to mark the sides or edges of these shapes that look like they are parallel. COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED a) b) c) 5. State which lines are parallel. a) A X B Y AB Geometry 7-6 F b) || d) R T U G S || E c) H L F G M || 109 Determining If Two Lines Are 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. N U O a) b) E B F c) A D M d) L R K W X S H V EF V Y || B || a) AB is parallel to K and KL is perpendicular to CD, so KL is also perpendicular to b) AB || and QR ^ Q C . , so,QR ^ B . R D L A B D C Mark the right angles on this rectangle. b) AD ^ AB and AD ^ || A 8. a) All the angles in a rectangle are right angles. J || 7. Complete the statements. C DC ^ AD and DC ^ , so AB || , so AD || c) Explain how you know that these pairs of sides are parallel. COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED 9. Circle the flags that contain parallel lines (not counting the edges of the flags). 110 Geometry 7-6 G7-7 Angle Relationships shared arm a b shared vertex straight angle A straight angle measures 180°. a adjacent angles Adjacent angles Ð a and Ð b have a shared vertex and arm. b linear pair The sum of the angles in a linear pair is 180°. 1. Match the diagrams to the names. Hint: The angles in a linear pair are also adjacent angles. straight angle: A. a adjacent angles: B. b linear pair: C. b a a b 2. Calculate 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 and Ð Ð and Ð Ð 4 1 2 3 4. Determine the sum of the angles formed by two lines that intersect at a right angle. ∠1 + ∠2 = 90 + 90 = So, ∠1 + ∠2 + ∠3 + ∠4 ∠3 + ∠4 = 90 + 90 = ° °+ °= ° ° 1 2 3 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 = So, ∠1 + ∠2 + ∠3 + ∠4 = ° and ∠3 + ∠4 = °. ° 30° 112 2 ° Calculate these angle sums to check your prediction. 95° 150° 1 3 ° 6. Predict the sum of the four angles around any point P. 4 COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED 150° 30° 30° + 150° + 30° + 150° = 85° 85° 95° 95° + 85° + 95° + 85° = Geometry 7-7 ∠XZY = ∠XZY = ∠A + ∠B + ∠C = 180 ∠A ∠A = 180 − (80 + 30 ) ∠F ∠A = 180 − ∠A =