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PLANE FIGURES: LINES AND ANGLES Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Angle bisectors and congruent angles can also be found given various information. Adjacent, complementary, supplementary and vertical angles can all be identified in the coordinate plane. Polygons can be measured to find their angles or missing angles. The sum of the interior angles of a polygon can found using a simple formula. How to use plane figures: lines and angles In the coordinate plane, there are 4 quadrants. In quadrant I, the x and y values are both positive. In quadrant II, the x value is negative and the y value is positive. In quadrant III, both the x and y values are negative. In quadrant IV, the x value is positive and the y value is negative. Angles in the coordinate plane can be measured using a tool called a protractor. • An angle is called an acute angle if it is less than 90°. • An angle is an obtuse angle if it is greater than 90°. • A right angle is exactly 90°. • A straight angle is exactly 180°. Triangles can be classified based on the measure of the angles within it. An acute triangle has all angles less than 90°, a n obtuse triangle has one angle that is over 90° and a right triangle has one right angle. For example, what type of angle is shown? What type of triangle would be made from this angle? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

The angle is an acute angle because it is less than 90°. If the arrowheads were connected, the triangle made would be an acute triangle. If the angle above was measured to be 30° and a line was drawn to cut the angle in half, the line would be called the angle bisector. The two angles formed by the angle bisector would be 15° each because together the angles would have to equal 30°. Intersecting Lines Make Angles Lines can also be drawn to make angles. • Perpendicular lines intersect to form right angles. • Other lines can cross the form adjacent angles, which are next to each other • Vertical angles, which are across from each other, Complementary angles, which add up to 90° and • Supplementary angles, which add up to 180°. • Lines that never cross a called parallel lines. For example, identify an adjacent and vertical angle, identify perpendicular and parallel lines and give one example of complementary and supplementary angles. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Given the lines, l, m, n, and o, the adjacent angles are 1 & 2, 3 & 4, 4 & 5, 5 & 8, 3 & 6, 6 & 7 and 7 & 8. The vertical angles are 3 & 8, 4 & 7 and 5 & 6. There are two sets of perpendicular lines, line l & line o and line m & line o. The parallel lines are line l and line m. Two complementary angles would be angles 4 & 5 and 6 & 7. The supplementary angles are 1 & 2. Sum of Angles • In a triangle, all the angles add up to 180°. • In a quadrilateral, the angles add up to 360°. • In a polygon with n sides, the sum of the interior angles = (n - 2) · 180°. • If given 3 angles of a quadrilateral, the fourth angle can be found by subtracting the known angles from 360°. • If two angles of a triangle are known, the third angle can be found by subtracting the known angles from 180°. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 1. What type of angle is shown? 2. What type of triangle is shown? 3. What is the sum of the interior angles for a hexagon? 4. What kinds of lines are shown? 5. For the diagram shown, name a pair of vertical, adjacent and supplementary angles. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

6. What is the missing angle for the quadrilateral and triangle shown? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.