Lesson 1.1 Building Blocks of Geometry

Transcription

1 Lesson 1.1 uilding locks of Geometry For xercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q. NQ. 3. nother name for NS is.. S is the of SQ. 5. is the midpoint of. 6. NS. 7. nother name for SN is. 8. Name all pairs of congruent segments in KLMN. Use the congruence symbol to write your answer. K N O 8 cm M 9. M(, 8) is the midpoint of. has coordinates (6, 1). Find the coordinates of. L 8 cm For xercises 10 and 11, use a ruler to draw each figure. Label the figure and mark the congruent parts. 10. and with M as the midpoint 11. and. is the midpoint of, with of both and. 6. cm 1.5 cm., not on, is the and.0 cm.,, and are midpoint of, with. not collinear. 1. Sketch six points,,,,,and F, no three of which are collinear. Name the lines defined by these points. How many lines are there? 13. In the figure below, {,, H, } is a set of four coplanar points. Name two other sets of four coplanar points. How many sets of four coplanar points are there? F G H ube iscovering Geometry ractice Your Skills HT 1 1

2 oordinate Geometry 1 The Midpoint For xercises 1 3, find the coordinates of the midpoint of the segment with each pair of endpoints. 1. (10, 3) and (, 1). (, 5) and (, 11) 3. (0, 3) and (5, 1). The midpoint of XY is (3, 5). The coordinates of point X are (1, 5). What are the coordinates of point Y? For xercises 5 and 6, use from the coordinate grid at right. 5. Find the midpoint of. 6. Find the points on that divide the segment into three congruent parts. Graph your solution and explain your method Find the midpoint of diagonal 8. Find the midpoint of. of the base XY in XYZ Z 8 6 X 5 Y 5 9. How many midpoints does a segment have? xplain your reasoning. 10. How many segments have the midpoint (, 3)? xplain your reasoning. HT 1 iscovering Geometry ractice Your Skills

3 Lesson 1. Finding ngles For xercises 1 5, use the figure at right to complete each statement. 1. is the of.. is the of. 3. is a of.. If m, then m. 5.. For xercises 6 9, use your protractor to find the measure of each angle to the nearest degree. 6. m O 7. m OT 8. m O 9. m TO For xercises 10 1, use your protractor to draw and then label each angle with the given measure. 10. m MNO m IG m z 160 O T For xercises 13 15, find the measure of the angle formed by the hands at each time :00 1. : : For xercises 16 and 17, mark each figure with all the given information m 90,, 17. m Q 90, Q TZ, T QZ, Q T T Q Z iscovering Geometry ractice Your Skills HT 1 3

4 Lesson 1.3 reating efinitions For xercises 1 9, match each term with one of the items (a to i) below. a. b.? c.? 90 1 d. e. f.?? g. h. i.? Q 1. Vertical angles. Obtuse angle 3. ight angle. omplementary angles 5. ongruent angles 6. Linear pair of angles 7. isected angle 8. erpendicular lines 9. ongruent segments 10. If m 13, m Q 77, and Q and are complementary, what can you conclude about and? xplain your reasoning. For xercises 11 13, sketch, label, and mark a figure showing each property , 3 1. Q 13. XY, X HT 1 iscovering Geometry ractice Your Skills

5 Lesson 1. olygons For xercises 1 8, complete the table. olygon name Number of sides Number of diagonals 1. Triangle Hexagon 5. Heptagon For xercises 9 and 10, sketch and label each figure. Mark the congruences. 9. oncave pentagon NT, with external diagonal T, and T. 10. quilateral quadrilateral QU, with Q U. For xercises 11 1, sketch and use hexagon F. 11. Name the diagonals from. 1. Name a pair of consecutive sides. 13. Name a pair of consecutive angles. 1. Name a pair of non-intersecting diagonals. For xercises 15 18, use the figures at right. MNOQ STUV 15. m N 16. V 17. m 18. ON O Q The perimeter of a regular pentagon is 31 cm. Find the length of each side. M N 16.1 S T V U iscovering Geometry ractice Your Skills HT 1 5

6 Lesson 1.5 Triangles For xercises 1 5, use the figure at right. Name a pair of 1. arallel segments. erpendicular segments 3. ongruent segments F. Supplementary angles 5. Linear angles G H I For xercises 6 and 7, sketch, label, and mark each figure. 6. Isosceles obtuse triangle TI with vertex angle T. 7. Scalene right triangle S with midpoints L, M, and N on S,, and S, respectively. For xercises 8 and 9, use your geometry tools to draw each figure. 8. cute isosceles triangle with vertex angle measuring Scalene right triangle GH. For xercises 10 1, use the graph at right. y 10. Locate F so that F is a right triangle. 11. Locate so that is an isosceles triangle. 1. Locate G so that G is scalene and not a right triangle. (0, 0) (8, 3) x (8, 0) 6 HT 1 iscovering Geometry ractice Your Skills

7 Lesson 1.6 Special Quadrilaterals For xercises 1 6, sketch, label, and mark each figure. 1. arallelogram G. Square SQ 3. hombus HOM with acute H.. Trapezoid T with T,, and,, and collinear. 5. Kite KIT with K KI and obtuse K. 6. ectangle NG with perimeter a b For xercises 7 10, name each polygon in the figure. ssume that the grid is square. 7. Square 8. arallelogram H G J I F 9. hombus 10. Kite For xercises 11 13, use the graph at right. y 11. Locate so that is a rectangle. 1. Locate so that is a trapezoid. 13. Locate G so that points,,, and G determine a parallelogram that is not a rectangle. (0, 0) (8, 3) x (8, 0) iscovering Geometry ractice Your Skills HT 1 7

8 Lesson 1.7 ircles For xercises 1, use the figure at right. 1. mq. m 3. mq. mq Q O 8 5. Sketch a circle with an inscribed pentagon. 6. Sketch a circle with a circumscribed quadrilateral. 7. circle with center (3, ) goes through (, ). Give the coordinates of three other points on the circle. y 8. Use a compass, protractor, and straightedge to draw circle O with diameter ; radius O with O ; O, the angle bisector of O, with on the circle; chords and ; and a tangent at. (, ) (3, ) x 9. Use a compass to construct a circle. Label the center. Sketch two parallel tangents. onnect the points of tangency. What do you notice about the chord? 10. Use your compass and protractor to make an arc with measure 50, an arc with measure 180, and an arc with measure 90. Label each arc with its measure. 11. Use your compass to construct two circles with different radii that intersect in two points. Label the centers and Q and the points of intersection and. onstruct quadrilateral Q. What type of quadrilateral is it? 8 HT 1 iscovering Geometry ractice Your Skills

9 Lesson 1.8 Space Geometry For xercises 1 and, draw each figure. 1. prism with a rectangular base.. cylinder with base diameter greater than height. For xercises 3 and, sketch the three-dimensional figure formed by folding each net into a solid. Name the solid. 3.. For xercises 5 and 6, sketch the section formed when each solid is sliced by the plane as shown The prism below is built with 1-cm 8. Find the lengths of x and y. cubes. How many cubes are completely hidden from sight, as seen from this angle? y 3 x iscovering Geometry ractice Your Skills HT 1 9

10 Lesson 1.9 Transformations In xercises 1 3, perform each transformation. 1. eflect TI across line.. otate L 70 clockwise 3. Translate NT by about Q. the given vector. I T L T N Q. and its reflected image,, are shown below. Use construction tools to locate the line of reflection,. xplain your method. 5. Given on the coordinate plane, complete the following transformations. a. Translate units right b. otate 90 counterclockwise c. eflect across and 3 units up. about the origin. the y-axis For exercise 5a above, which of the following statements are true? a. b. c. 10 HT 1 iscovering Geometry ractice Your Skills