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# The Polygon Angle-Sum Theorems

1. 2. 3. Find the sum of the measures of the angles in an octagon. 4. A pentagon has two right angles, a 100° angle and a 120° angle. What is the measure of its fifth angle? 5. Find m ABC . 6. XBC is an exterior angle at vertex B . Find m XBC. quadrilateral ABCD ;

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## The Polygon Angle-Sum Theorems

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1. 1.2. 3. Find the sum of the measures of the angles in an octagon. 4. A pentagon has two right angles, a 100° angle and a 120° angle. What is the measure of its fifth angle? 5. Find m ABC. 6.XBC is an exterior angle at vertex B. Find m XBC. quadrilateral ABCD; AB, BC, CD, DA The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-5 QUIZ3-4, 3-5 & 3-8Friday For Exercises 1 and 2, if the figure is a polygon, name it by its vertices and identify its sides. If the figure is not a polygon, explain why not. not a polygon because two sides intersect at a point other than endpoints 1080 140 ABCDEFGHIJ is a regular decagon. 144 36 3-5

2. 1. Are lines 1 and 2 parallel? Explain. 2. Are the lines x + 4y = 8 and 2x + 6y = 16 parallel? Explain. 3. Write an equation in point-slope form for the line parallel to –18x + 2y = 7 that contains (3, 1). 4. Are the lines y = x + 5 and 3x + 2y = 10 perpendicular? Explain. 5. Write an equation in point-slope form for the line perpendicular to y = – x – 2 that contains (–5, –8). 1 6 Slopes of Parallel and Perpendicular Lines GEOMETRY LESSON 3-7 Yes; the lines have the same slope and different y-intercepts. No; their slopes are not equal. y – 1 = 9(x – 3) 2 3 Yes; the product of their slopes is –1. y + 8 = 6(x + 5) 3-7

3. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 (For help, go to Lesson 1-7.) Use a straightedge to draw each figure. Then use a straightedge and compass to construct a figure congruent to it. 1. a segment 2. an obtuse angle 3. an acute angle 4. a segment 5. an acute angle 6. an obtuse angle Use a straightedge to draw each figure. Then use a straightedge and compass to bisect it. Check Skills You’ll Need 3-8

4. 1.2. 3.4. 5.6. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 Solutions 3-8

5. Step 1: With the compass point on point H, draw an arc that intersects the sides of H. Step 3: Put the compass point below point N where the arc intersects HN. Open the compass to the length where the arc intersects line . Keeping the same compass setting, put the compass point above point N where the arc intersects HN. Draw an arc to locate a point. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 Quick Check Examine the diagram. Explain how toconstruct 1 congruent to H. Use the method learned for constructing congruent angles. Step 2: With the same compass setting, put the compass point on point N. Draw an arc. Step 4: Use a straightedge to draw line m through the point you located and point N. 3-8

6. Construct a quadrilateral with both pairs of sides parallel. Step 1: Draw point A and two rays with endpoints at A. Label point B on one ray and point C on the other ray. Step 2: Construct a ray parallel to AC through point B. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 3-8

7. Step 3: Construct a ray parallel to AC through point C. Step 4: Label point D where the ray parallel to AC intersects the ray parallel to AB. Quadrilateral ABDC has both pairs of opposite sides parallel. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 Quick Check (continued) 3-8

8. In constructing a perpendicular to line at point P, why must you open the compass wider to make the second arc? With the compass tip on A and B, the same compass setting would make arcs that intersect at point P on line . Without another point, you could not draw a unique line. With the compass tip on A and B, a smaller compass setting would make arcs that do not intersect at all. Once again, without another point, you could not draw a unique line. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 Quick Check 3-8

9. Examine the construction. At what special point does RG meet line ? This means that RG intersects line at the midpoint of EF, and RG is the perpendicular bisector of EF. Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 Point R is the same distance from point E as it is from point F because the arc was made with one compass opening. Point G is the same distance from point E as it is from point F because both arcs were made with the same compass opening. Quick Check 3-8

10. 1. Construct a line through D that is parallel to XY. 2. Construct a quadrilateral with one pair of parallel sides of lengths p and q. 3. Construct the line perpendicular 4. Construct the line perpendicular to line m at point Z. to line n through point O. Answers may vary. Sample given: Answers may vary. Sample given: Constructing Parallel and Perpendicular Lines GEOMETRY LESSON 3-8 Draw a figure similar to the one given. Then complete the construction. 3-8

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