# The Polygon Angle-Sum Theorems

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The Polygon Angle-Sum Theorems
GEOMETRY LESSON 3-5 QUIZ 3-4, 3-5 & 3-8 Friday 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. 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 not a polygon because two sides intersect at a point other than endpoints 1080 140 ABCDEFGHIJ is a regular decagon. 144 36 3-5

Slopes of Parallel and Perpendicular Lines
GEOMETRY LESSON 3-7 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 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

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

Constructing Parallel and Perpendicular Lines
GEOMETRY LESSON 3-8 Solutions 3-8

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

Constructing Parallel and Perpendicular Lines
GEOMETRY LESSON 3-8 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. 3-8

Constructing Parallel and Perpendicular Lines
GEOMETRY LESSON 3-8 Quick Check (continued) 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. 3-8

Constructing Parallel and Perpendicular Lines
GEOMETRY LESSON 3-8 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. Quick Check 3-8

Constructing Parallel and Perpendicular Lines
GEOMETRY LESSON 3-8 Examine the construction. At what special point does RG meet line ? 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. This means that RG intersects line at the midpoint of EF, and RG is the perpendicular bisector of EF. Quick Check 3-8

Constructing Parallel and Perpendicular Lines
GEOMETRY LESSON 3-8 Draw a figure similar to the one given. Then complete the construction. 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 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: 3-8

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