3 rd Six Weeks

Transcription

1 Geometry

2 3 rd Six Weeks MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Nov Angle Measures in Polygons Class: Wksht #1 6- Properties of Parallelograms Class: Wksht # 6-3 Proving Parallelograms Class: Wksht #3 6-3 Proving Parallelograms Class: Wksht #3 Quiz Chapter 6 sections 1-3 Class: Review HW: Watch video 6-, take notes HW: Watch video 6-3, take notes HW: Complete classwork HW: Complete Classwork HW: Watch video 6-4/6-5, take notes /6-5 Rhombus, Rectangles, and Squares Test #7 6-6 Trapezoids and Kites 6-6 Trapezoids and Kites Guess the Quadrilateral Quiz HW:Review for Test HW: Watch Video 6-6, Take Notes HW: Watch video Guess the quad, take notes HW: Watch video Guess the quad, take notes Finish Guess the quad Review Turn in Guess the quad Test #8 Thanksgiving Thanksgiving Thanksgiving HW: Review 30 Dec Chapter 9 Intro to Proportions 9-1 Similar Polygons 9-3 Proving Triangles Similar 9-3 Proving Triangles Similar 9-5 Proportions in Triangles HW: Watch video 9-1, Take Notes HW: Watch Video 9-3, take notes HW: Watch Video 9-5, take notes HW: Watch Video 9-5, take notes HW: Complete classwork, start review Review HW: Study Review Test #9 Final Exam Review Scavenger Hunt Final Exam Review Scavenger Hunt Final Exam Review Final Exam Review FINAL EXAMS FINAL EXAMS FINAL EXAMS FINAL EXAMS Each night after watching video, classwork should be completed.

3 Worksheet 6-1 Polygon Angle-Sum Theorems No rounding. All numerical answers must be proper fractions, integers, mixed numbers, terminating decimals, or simplified radicals. The number of sides of a convex polygon is given. Find the sum of the measures of the interior angles of each polygon. 1) 8 ) 1 3) 14 4) 16 5) p The sum of the measures of the interior angles of a convex polygon is given. Find the number of sides of each polygon. 6) 700 7) ) 610 9) ) 340 The number of sides of a regular polygon is given. Find the measure of each interior angle of each polygon. 11) 7 1) 9 13) 11 14) 15 15) 17 Find the exact measure of each exterior angle of the regular polygon. 16) pentagon 17) heptagon 18) decagon 19) 18-gon 0) 0-gon 1) Home plate on a baseball field has three right angles and two congruent angles. Find the measure of the two congruent angles. ) The sum of the measures of seven angles of an octagon is Find the measure of the eighth angle. 3) How many sides does a regular polygon have if each exterior angle has a measure of 15? 4) How many sides does a regular polygon have if each interior angle has a measure of 108? 5) Find the number of sides of a polygon if the sum of the measures of its interior angles is twice the sum of the measures of its exterior angle. 6) The measure of each interior angle of a regular polygon is eight times that of an exterior angle. How many sides does the polygon have? 7) In quadrilateral ABCD the measures of, A, B, C, and D are the ratio of 1::3:4, respectively. Find the measures of the four angles. Page 1

4 Find the value of x. 8) 9) 30) 31) 3) 33) 34) 35) Page

5 Worksheet 6- Properties of Parallelograms No rounding. All numerical answers must be proper fractions, integers, mixed numbers, terminating decimals, or simplified radicals. ABCD is a parallelogram. State the reason that justifies each conclusion. 1) DAB DCB ) BE ED 3) AD BC 4) CD AB D E C Complete each statement. 5) If AD 0, BC =? 6) If madc 115, m ABC =? 7) If BD, DE =? 8) If AE 18, AC =? 9) If mdab 75, m ADC =? 10) If mdca 30, m CAB =? 11) If BD 10 and AE 3, AC =? 1) If mabc ( mbcd ), m ADC =? 13) If madc 130 and macb 35, m DCA =? A #1-#13 B Find the measure of each angle in parallelogram MNST. M 18 T 14) m TMN 15) m TSN 16) m MST 17) m SPN N 30 P 95 S Complete each statement for parallelogram KLMN. 18) If KN 3x 5 and LM x 9, KN =? x 19) If KL and MN x 9, KL =? x 0) If KL 8 and MN, x =? 1) If mk (4x 11) and ml (6x 1), m K =? ) If mk 97 and mm (x 1), x =? K N #18-#3 L M 3x 3) If ml ( x 40) and mn 4, m L=? A B C 4) If AC XY and altitude, BD, of BXY is 8, what are the lengths of the altitudes of ACX and CXY from vertices A and C respectively? 5) Given: parallelogram ABCD with AB x 5 and CD x 7. Find AB. E X D Y F 6) Given parallelogram ABCD with AB x, CD 3y 4 sides of the parallelogram., BC x 7, and AD y. Find the lengths of the Draw a picture of each quadrilateral, to determine if it is a parallelogram by one Theorems. Be able to explain your selection. 7) In quadrilateral BLOT, BL ll TO, mbto 80, and mlot 100 8) In quadrilateral JOKE, JO EK, m OJE 65 9) In quadrilateral SLOW, SL LO OW SW., and m JEK ) In quadrilateral MOAT, MA intersects OT at R, MR RA, and TR OR. 31) In quadrilateral CRAB, m RCB 60, m CBA 10, and m CRA 10. Page 3

6 Find the value of x and y that ensure each quadrilateral is a parallelogram. 3) 33) 34) 4x 4y 35) 36) 37) 6 3x 5y 3 6 x y x 5y 53 38) 39) 40) x Find all the possible coordinates(3) for the fourth vertex of a parallelogram with the given vertices. Then draw the parallelogram on the graph. 41) 4) Page 4

7 Worksheet 6-3 Proving that a Quadrilateral is a Parallelogram WXYZ is a parallelogram. State the Theorem that justifies each conclusion. Use the figure below. 1) XWZ XYZ ) XP PZ 3) XY WZ 4) WX YZ Complete each statement that would make the figure a parallelogram. 5) If 15 6) If WZY 110 YZ, then WX m, then m WXY 7) If XZ 6, then XP X P Y 8) If 18 9) If XWZ 75 PY, then WY m, then m WXY mwxy mxyz, then m WZY 10) If W Z Find the measure of each angle in the parallelogram PQRS. 11) m STP 1) m PSR 13) m PQR 14) m PSQ P Q 37 T S R IV. Complete each statement. 15) If QR x 3, PS 3x 5, QR 16) If QP 3x 4, RS 4x 3, RS x 17) If RS, PQ 1, x 3 m P 5x 5, ms 3x 15, mp m Q 7x 3, ms 10x 45, x 18) If 19) If 0) If m P x 6, mr 55, x P Q S R Page 5

8 6-3 Proving Parallelograms Coordinate Parallelograms Determine if it is a parallelogram with the reason given. Explain and show proof. 1) A1,4, B1, 1, C 1, 5, D 3,0, by Def. ) E6,, F, 4, G 3,1, H 1,3 length, by side 3) I,, J 3,3, K 4,, L1, 3 by diagonals 4) M,, N 3, 5, O 4, 6, P 5,1 1 side parallel and congruent. Page 6

9 5) Q4, 6, R3,, S,6, T 5, Any method 6) U 4, 3, V 3,3, W 3,, X, 4 method Any 7) Q1,4, U 5,1, A, 5, D4, Any method 8) A 5, 4, B1,5, C 4,3, D, 6 method Any Page 7

10 Review Chapter 8 sections 1 to 3 Name 1 to 4, Prove each of the figures a parallelogram by the stated method. 1) By definition ) Opposite sides congruent 3) Diagonals bisect each other 4) Any method 5) Parallelogram DUMB has DU 3x 6, DB 6x 3, and BM 81. What is the length of UM. 6) Find the measure of each side 7) Find the measure of each angle of the parallelogram. of the parallelogram. S T P O Page 8

11 8) The sum of the exterior angles of a hexagon is 8c. What is the value of c. 9) A convex pentagon has angles of 100,130,7w, 80, and 4.5w. What is the sum of these interior angles? What is the value of w? 10) The measures of the exterior angles of a convex hexagon are 45, 60, x, 3x, 7x, and 90. What is the measure of the largest exterior angle? 11) The measures of the interior angles of a convex decagon are 150, 145, 130, 34x, 35x, 135,160, 10,30x, and 1x. What is the measure of the smallest interior angle. Find the value of n. 1) Each interior angle of the regular n-gon has a measure of ) Each interior angle of the regular n-gon has a measure of ) Each exterior angle of the regular n-gon has a measure of 5. 15) Each exterior angle of the regular n-gon has a measure of 1. 16) Solve for the value of z. 17) Fill in the following table. Find the sum of the measures of the interior angles of each convex polygon. 18) 30-gon 19) 15-gon 0) 60-gon 1) -gon The measures of an exterior angle of a regular polygon is given. Find the number of sides of the polygon. ) 4 3) 0 4) 5 5) 9 Page 9

12 The number of sides of a regular polygon is given. Find the measure of an interior angle and an exterior angle for each polygon. 6) 18 7) 36 8) 10 9) 40 Use Polygon ABCDEF to answer each question. (Vocabulary) 30) Name the vertices of the polygon. 31) Name the angles of the polygon. 3) Name the sides of the polygon. 33) Is the polygon convex or concave. 34) Name the polygon according to the number of sides it has. 35) Is the polygon regular? Explain you answer. Find the value of x and each angle measure. 3x+0 x+60 4x+0 36) 37) 38) 6x 3x+1 x+4 5x+0 4x+13 6x 6x+0 8x 39) Solve for the values of w, x, y and 40) for what value of d is the z in the parallelogram quadrilateral a parallelogram? 41) For what value of g is PQRS a parallelogram? Determine the value of variables so that the figure is a parallelogram. x y 4) 15 43) 44) 45) 5 y x 85 Page 10