Properties of Quadrilaterals

Transcription

1 MIAP Chapter 6: Linear functions Master 6.1a Activate Prior Learning: Properties of Quadrilaterals A quadrilateral is a polgon with 4 sides. A trapezoid is a quadrilateral that has eactl one pair of parallel sides. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. All parallelograms have: opposite sides equal opposite angles equal diagonals that bisect each other A rectangle is a parallelogram with 4 right angles. It has all the properties of a parallelogram and its diagonals are equal. A rhombus is a parallelogram with 4 equal sides. It has all the properties of a parallelogram and its diagonals are perpendicular. A square is a parallelogram with 4 equal sides and 4 right angles. A square has all the properties of a parallelogram, a rectangle, and a rhombus. Check Your Understanding Indicate whether each statement is true or false. If a statement is false, eplain wh. 1. The diagonals of a rectangle bisect each other. 2. A square is a rhombus.. A trapezoid is a parallelogram. 4. The diagonals of a parallelogram are equal. 5. The diagonals of a rhombus bisect each other. 6. A parallelogram with one right angle is a rectangle. 7. All squares are rectangles. 8. Some trapezoids are squares. 9. A rectangle with two adjacent sides equal is a square. 1 P age

2 MIAP Chapter 6: Linear functions Master 6.1b Activate Prior Learning: Operations with Rational Numbers To add or subtract two rational numbers, use equivalent fractions that have like denominators. 2 To add : 2 Write as a fraction with denominator is a multiple of and 1. is a common denominator. 1 = 9 So, = Add the numerators = To multipl two rational numbers, we do not need a common denominator. 8 To multipl 5 15 : 8 Notice that the numerator and denominator have common factor To simplif first, divide the numerator and denominator b. 1 8 = = 1 and 15 = = 8 25 Multipl the numerator and multipl the denominator. Check Your Understanding 1. Simplif. a) 2 4 b) 7 2 c) 5 2 d) Simplif a) 7 b) 9 c) d) P age

3 Master 6.5a Answers Master 6.1a 1. True 2. True. False; a trapezoid has onl one pair of parallel sides. 4. False; onl the diagonals of a rectangle and a square are equal. 5. True 6. True 7. True 8. False; a square has both pairs of opposite sides parallel. A trapezoid has onl one pair of parallel sides. 9. True Master 6.1b 1. a) 11 4 b) 1 2 c) 1 2. a) 15 b) 21 c) d) 2 d) P age

4 Lesson 6.1 Check Your Understanding Outcome R pgs Slope is another wa of saing rate of change. Determine the slope of each line segment. Slope = rise Write the fraction in simplest form. run a) b) 2. Draw a line segment with each slope. a) 4 9 start at point (-, -2) b) 8 Start at point (2, ) c) Draw a line with a positive slope, negative slope, zero slope and undefined slope. Label each. 4 P age

5 . Determine the slope of the line that passes through E(4, 5) and F(8, 6). Solution Sketch the line. 4. Tom has a part-time job. He recorded the hours he worked and his pa for different das. Tom plotted these data on a grid. a) What is the slope of the line through these points? b What does the slope represent? c) How can the answer to part b be used to determine: i) how much Tom earned in 1 2 hours? ii) the time it took Tom to earn $0? Formula 2 1 Slope of PQ = HW pg 9, A#4-9, B#11,1,17,2 C #1 5 P age

6 Ch 6.2 Parallel and Perpendicular slopes Outcome R pg Line EF passes through E(, 2) and F( 1, 6). Line CD passes through C( 1, ) and D(1, 7). Line AB passes through A(, 7) and B( 5, 2). Sketch the lines on the same grid. Are the parallel? Justif our answer. Solution Use the formula for the slope of a line through points with coordinates ( 1, 1 ) and ( 2, 2 ): 2 1 Slope = Line ST passes through S( 2, 7) and T(2, 5). Line UV passes through U( 2, ) and V(7, 6). a) Are these two lines parallel, perpendicular, or neither? Justif our answer. b) Sketch the lines to verif our answer to part a. 6 P age

7 . a) Determine the slope of a line that is perpendicular to the line through G( 2, ) and H(1, 2). b) Determine the coordinates of J so that line GJ is perpendicular to line GH. 4. EFGH is a parallelogram. Is it a rectangle? Justif our answer. Hint: A parallelogram has opposite sides equal. It is a rectangle if its angles are right angles. To check whether EFGH is a rectangle, determine whether two intersecting sides are perpendicular. Determine whether EF is perpendicular to FG. HW pg 49 A #-6 B # 8,9,11,1,18,20 C #2, 24 7 P age

8 Ch 6.4 Slope Intercept Form Outcome R6/R7 1. The graph of a linear function has slope Write an equation for this function. 7 and -intercept Graph the linear function with equation: = P age

9 . Write an equation to describe this function. Verif the equation. 4. To join the local gm, Karim pas a start-up fee of $99, plus a monthl fee of $29. a) Write an equation for the total cost, C dollars, for n months at the gm. b) Suppose Karim went to the gm for 2 months. What was the total cost? c) Suppose the total cost was $505. For how man months did Karim use the gm? d) Could the total cost be eactl $600? Justif our answer. 6.4 HW Pg 62 #4-6 #7,12,14,18 # P age

10 Master 6.12 Lesson 6.5 Check Your Understanding a 6.5 Slope-Point form outcome R6/R7 pg = m( 1) point slope form 1.a) Describe the graph of the linear function with this equation: + 1 = b) Graph the equation. 1 ( 2) 2 2. a) Write an equation in slope-point form for this line. b) Write the equation in part a in slope-intercept form. What is the -intercept of this line? 10 P age

11 . A temperature in degrees Celsius, c, is a linear function of the temperature in degrees Fahrenheit, f. The boiling point of water is 100 C and 212 F. The freezing point of water is 0 C and 2 F. a) Write a linear equation to represent this function. b) Use the equation to determine the temperature in degrees Celsius at which iron melts, 2795 F. 4. Write an equation for the line that passes through S(2, ) and is: a) parallel to the line = + 5 b) perpendicular to the line = HW pg 72 #4-6 #7,8,9,12,2-25 #26-27 Assess our understanding pg P age

12 6.6 General form of a linear Equation outcome r6/r7 pg Write each equation in general form. 1 a) 4 b) 2 ( 4) 2 2. a) Determine the - and -intercepts of the line whose equation is: = 0 b) Graph the line. c) Verif that the graph is correct.. Determine the slope of the line with this equation: = 0 4. Akeego is making a ribbon shirt. She has 60 cm of ribbon that she will cut into 5 pieces with 2 different lengths: 2 pieces have the same length and the remaining pieces also have equal lengths. a) Generate some data for this relation showing the possible lengths of the pieces. 12 P age

13 Lengths of pieces, (cm) Lengths of 2 pieces, (cm) b) Graph the data. c) Write an equation for the relation in general form. d) i) Can each of 2 pieces be 18 cm long and each of pieces be cm long? ii) Can each of 2 pieces be cm long and each of pieces be 18 cm long? Use the graph and the equation to justif our answers. 6.6 HW pg 84 #4-6 #9, 12, 14, 16,22 # P age