You MUST know the big 3 formulas!

Transcription

1 Name 3-13 Review Geometry Period Date Unit 3 Lines and angles Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation y = mx + b Writing the equation of a line given a graph. Graphing Linear Equation 3-2 Point Slope Form y y 1 = m(x x 1 ) 3-3 Using slope and y intercept to determine if line are parallel, perpendicular, or the same line. Same slope Parallel Opposite reciprocal slope Perpendicular Same slope and y-intercept same line 3-4 Writing equations of lines. Parallel lines Same slope as original, use one point on the line then sub into y y 1 = m(x x 1 ) Perpendicular lines opposite reciprocal slope of original, use point on the line then sub into y y 1 = m(x x 1 ) 3-5 Slope of a line using slope formula m = y 2 y 1 x 2 x 1 Watch out for common mistakes! 1. Y s are on top! 2. Double negatives! Use your CALCULATOR! 3. Simplify fractions! 3-6 Distance and Midpoint Distance or length: d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 You MUST know the big 3 formulas! Midpoint Formula: M = ( x 1+x 2, y 1+y 2 ) 2 2 Watch out for common mistakes! 1. Take it slow, show all steps. 2. Don t forget parentheses and comma for Midpoint! 3-7 Writing equation of perpendicular Bisector. Find slope of given line, take the opposite reciprocal. Calculate Midpoint of given line. Sub the new slope and midpoint into y y 1 = m(x x 1 ) make sure you sub in MIDPOINT. Not the points on line 3-8 QUIZ- Make sure you look at all your mistakes! Simplify Radicals make prime factor tree pairs go outside multiply by anything already outside. 3-9 Angles and notation Vertical angles Across from each other, always congruent Angles at a point Make a full circle add up to 360 degrees. Linear pairs Adjacent and supplementary add up to 180 degrees. Supplementary angles two angles that add up to 180 degrees. Complementary angles two angles that add up to 90 degrees Angles on a transversal Alt. Interior, Alt. Exterior, Corresponding angles are if the lines are. Same-side Int., Same side Ext. are supplementary if the lines are Justifying parallel lines When justifying parallel lines you need to include 1. Type of angle pair 2.Relationship 3. Conclusion 3-12 Construction of parallel lines ( with justification) -Construction works because we are copying an angle into the corresponding position on the new line.

2 Station 1: Linear Equations 1) Write the equation of a line that contains the point (2,-4) and is perpendicular to the line whose equation is:. 2) Are the two lines represented below parallel, perpendicular or neither? JUSTIFY your answer. Equation 1: y 5 = 4 (x + 2) 5 Equation 2: y 2 = 4 (x + 5) 5 3) Write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,8) and (11, -4) 4) Write the equation of a line that is parallel to the line y = 1 x + 4 and goes through the point (-8, 3) 2

3 Station 2: Slope, Midpoint, Distance 1) Line segment AB has endpoints A(2, 8), and B(-2, 2). Line segment CD has endpoints C(6, 3) and D(-6, 7). Do AB and CD have the same midpoint? 2) Line segment JK has endpoints J(0,0) and K(12, 9). Line segment UV has endpoints U(2, 3) and V(5, 7). Which segment is longer (has a greater length)? a) What formula will you use to answer this question? How do you know? b) Which segment is longer (has a greater length)? Show all work and leave answers in simplest radical form 3) Simplify the cube roots: a 3

4 4) Samantha wants to know if the line A, that passes through points (15, -9) and (9, -9) is parallel to line B that passes through points (-4, -1) and (3, -1). a) What formula will you use to answer this question? How do you know? b) Is line A parallel to line B? Show all work. 5) If AB are the endpoints of a line with midpoint M, and A(3,0) and M(-2,8), find the other endpoint. 6) In circle G, diameter HI has endpoints H (2a +3, 5b - 2) and I (6a - 1, 7b+4). a) Find the coordinates of point G in terms of A and B in simplest form. b) Find the slope of HI in terms of A and B 7) Find the slope of the line that passes through the points M(-9, -8) and N(1, -4). Put your slope in simplest form. 8) Find the length of segment AB if A(-4,4) and B(10,-2) in simplest radical form!

5 Station 3: Special Angle Pairs and parallel lines 1) Given the accompanying diagram: Identify a pair of parallel lines in the figure if 3 7. Justify your answer. 2) In the diagram below, line p intersects line m and line n. If and, lines m and n are parallel when x equals 1) ) 15 3) ) 105 3) Investigate the two drawings. What angle relationships are shown for each drawing? State whether AB is parallel to CD in each drawing. EXPLAIN YOUR REASONING. Extend your lines!

6 4) Lines j and k intersect at point p forming angles 1, 2, 3, and 4. If the m< 3 = 25 what is the m<1? What special angle pair are they? Sketch first! 5) Solve for x, given that the two lines cut by a transversal are parallel, and < 1 = x + 10 and < 7 = 2x 40 6) A linear pair of angles are in a 3:6 ratio. Find each angle. 7) Solve for angle a:

7 8) Given that lines AB and CD intersect to form the angles below solve for x. 9) Solve for z. 10) Construct a line parallel to given line through the Point R. Justify the construction (how do you know the lines are actually parallel?)

8 Use your skills! State answers here m 1 m 3 m 5 m 7 m 9 m 11 m 2 m 4 m 6 m 8 m 10 m 12