Math 366 Chapter 12 Review Problems

Transcription

1 hapter 12 Math 366 hapter 12 Review Problems 1. ach of the following figures contains at least one pair of congruent triangles. Identify them and tell why they are congruent. a. b. G F c. d. e. f. 1

2 hapter 12 g. h. 2. In the following figure, is a square and F. What kind of figure is F? Justify your answer. F 3. If is a trapezoid, F // and is a diagonal, what is the relationship F between and? Why? F F 2

3 hapter For each of the following figures, show that appropriate triangles are similar and find x and y. x 3 in. 8 in. 5 in. 4 ft 6 ft 7 ft 5 ft y x 5. etermine whether each of the following is true or false. If false, explain why. a. radius of a circle is a chord of the circle. b. If a radius bisects a chord of a circle, then it is perpendicular to the chord. 6. person 2 m tall casts a shadow 1 m long when a building has a 6-m shadow. How high is the building? 7. Which of the following polygons can be inscribed in a circle? a. rhombus b. regular hexagon c. regular octagon d. ased on your answers, make a conjecture about what kinds of polygons can be inscribed in a circle. 3

4 hapter etermine the vertical height of the playground slide shown in the following figure. 1.5 m h 2 m 8 m 9. Find the distance d across the river sketched. d 20 m 64 m 16 m 10. If two lines on a coordinate plane are parallel, must their slopes always be equal? Why or why not? 11. In an equilateral triangle, what must be true about all midsegments? 4

5 hapter For each of the following, write the equation of the line determined by the given pair of points. a. (2, -3) and (-1, 1) b. (-3, 0) and (3, 2) 13. Use slope to determine whether there is a single line through the points with coordinates (4, 2), (0, -1), and (7, -5). xplain your reasoning. 14. Solve each of the following systems, if possible. If the system does not have a unique solution, explain why not. x+ 2y = 3 x y + = 1 x 2y = 1 a. b. 2 3 c. 2x y = 9 4y 3x= 2 4y 2x= Solve for x in the following: a. b m 4 m 2 m x x 16. On a test, a student wrote instead of. Is this answer correct? Why? 17. student asks if there are any constructions that cannot be done with a compass and a straightedge. How do you answer? 5

6 hapter student draws the following figure and claims that because every triangle is congruent to itself, we can write. What is your response? 19. student asks whether there is an similarity condition for quadrilaterals. How do you respond? 20. student says that a vertical line has an infinite slope. How do you respond? 6

7 hapter 12 e able to do the following constructions: ircle onstruction (given center and radius) Segment onstruction onstruct a segment congruent to the given segment onstructing a Triangle Given Three Sides onstruct using the three sides. onstructing ongruent ngles onstruct 7

8 hapter 12 onstructions Involving Two Sides and an Included ngle of a Triangle onstruct using two sides and the included angle. onstruction of the Perpendicular isector of a Segment onstruct a perpendicular bisector of. onstruction of a ircle ircumscribed bout a Triangle onstruct a circle circumscribed about. 8

9 hapter 12 onstructing Parallel Lines Rhombus method onstruct a line through P parallel to l. P l orresponding ngle method onstruct a line through P parallel to l. P l onstructing ngle isectors onstruct an angle bisector of. onstructing Perpendicular Lines onstruction of a Perpendicular to a Line through a Point not on the Line onstruct a line through P, perpendicular to line l (P is not a point on l). P l onstruction of a Perpendicular to a Segment through the Midpoint of the Segment This construction was done in section

10 hapter 12 onstruction of a Perpendicular to a Segment through a Point on the Segment onstruct a line through P, perpendicular to line l (P is a point on l). P l onstructing a ircle Inscribed in a Triangle. Inscribe a circle in. onstruction Separating a Segment into ongruent Parts Separate into three congruent parts. 10