Lesson Menu FiveMinute Check over Lesson 2 9
- Slides: 42
Lesson Menu Five-Minute Check (over Lesson 2– 9) Mathematical Practices Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate 2. 15: Perpendicular Postulate Example 1: Real-World Example: Construct Distance From Point to a Line Example 2: Distance from a Point to a Line on Coordinate Plane Key Concept: Distance Between Parallel Lines Theorem 2. 25: Two Line Equidistant from a Third Example 3: Distance Between Parallel Lines
Over Lesson 2– 9 Given 9 13, which segments are parallel? ___ ___ ___ A. AB || CD B. FG || HI C. CD || FG D. none
Over Lesson 2– 9 Given 9 13, which segments are parallel? ___ ___ ___ A. AB || CD B. FG || HI C. CD || FG D. none
Over Lesson 2– 9 Given 2 5, which segments are parallel? ___ ___ ___ __ A. AB || CD B. CD || FG C. FG || HI D. none
Over Lesson 2– 9 Given 2 5, which segments are parallel? ___ ___ ___ __ A. AB || CD B. CD || FG C. FG || HI D. none
Over Lesson 2– 9 ___ If m 2 + m 4 = 180, then AB || CD. What postulate supports this? A. If consecutive interior s are supplementary, lines are ||. B. If alternate interior s are , lines are ||. C. If corresponding s are , lines are ||. D. If 2 lines cut by a transversal so that corresponding s are , then the lines are ||.
Over Lesson 2– 9 ___ If m 2 + m 4 = 180, then AB || CD. What postulate supports this? A. If consecutive interior s are supplementary, lines are ||. B. If alternate interior s are , lines are ||. C. If corresponding s are , lines are ||. D. If 2 lines cut by a transversal so that corresponding s are , then the lines are ||.
Over Lesson 2– 9 ___ __ If 5 14, then CD || HI. What postulate supports this? A. If corresponding s are , lines are ||. B. If 2 lines are ┴ to the same line, they are ||. C. If alternate interior s are , lines are ||. D. If consecutive interior s are supplementary, lines are ||.
Over Lesson 2– 9 ___ __ If 5 14, then CD || HI. What postulate supports this? A. If corresponding s are , lines are ||. B. If 2 lines are ┴ to the same line, they are ||. C. If alternate interior s are , lines are ||. D. If consecutive interior s are supplementary, lines are ||.
Over Lesson 2– 9 ___ __ Find x so that AB || HI if m 1 = 4 x + 6 and. m 14 = 7 x – 27. A. 6. 27 B. 11 C. 14. 45 D. 18
Over Lesson 2– 9 ___ __ Find x so that AB || HI if m 1 = 4 x + 6 and. m 14 = 7 x – 27. A. 6. 27 B. 11 C. 14. 45 D. 18
Over Lesson 2– 9 Two lines in the same plane do not intersect. Which term best describes the relationship between the lines? A. parallel B. perpendicular C. skew D. transversal
Over Lesson 2– 9 Two lines in the same plane do not intersect. Which term best describes the relationship between the lines? A. parallel B. perpendicular C. skew D. transversal
Mathematical Practices 2 Reason abstractly and quantitatively. 4 Model with mathematics. Content Standards G. CO. 12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc. ). G. MG. 3 Apply geometric methods to solve problems (e. g. , designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
You proved that two lines are parallel using angle relationships. • Find the distance between a point and a line. • Find the distance between parallel lines.
• equidistant
Construct Distance From Point to a Line CONSTRUCTION A certain roof truss is designed so that the center post extends from the peak of the roof (point A) to the main beam. Construct and name the segment whose length represents the shortest length of wood that will be needed to connect the peak of the roof to the main beam. The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point. Locate points R and S on the main beam equidistant from point A.
Construct Distance From Point to a Line Locate a second point not on the beam equidistant from R and S. Construct AB so that AB is perpendicular to the beam. Answer:
Construct Distance From Point to a Line Locate a second point not on the beam equidistant from R and S. Construct AB so that AB is perpendicular to the beam. ___ Answer: The measure of AB represents the shortest length of wood needed to connect the peak of the roof to the main beam.
KITES Which segment represents the shortest distance from point A to DB? A. AD B. AB C. CX D. AX
KITES Which segment represents the shortest distance from point A to DB? A. AD B. AB C. CX D. AX
Distance from a Point to a Line on a Coordinate Plane COORDINATE GEOMETRY Line s contains points at (0, 0) and (– 5, 5). Find the distance between line s and point V(1, 5). Step 1 Find the slope of line s. Begin by finding the slope of the line through points (0, 0) and (– 5, 5) V(1, 5) (0, 0)
Distance from a Point to a Line on a Coordinate Plane Then write the equation of this line by using the point (0, 0) on the line. Slope-intercept form m = – 1, (x 1, y 1) = (0, 0) Simplify. The equation of line s is y = –x.
Distance from a Point to a Line on a Coordinate Plane Step 2 Write an equation of the line t perpendicular to line s through V(1, 5). Since the slope of line s is – 1, the slope of line t is 1. Write the equation for line t through V(1, 5) with a slope of 1. Slope-intercept form m = 1, (x 1, y 1) = (1, 5) Simplify. Subtract 1 from each side. The equation of line t is y = x + 4.
Distance from a Point to a Line on a Coordinate Plane Step 3 line s: Solve the system of equations to determine the point of intersection. y = –x line t: (+) y = x + 4 2 y = 4 Add the two equations. y= 2 Divide each side by 2. Solve for x. 2 = –x – 2 = x Substitute 2 for y in the first equation. Divide each side by – 1. The point of intersection is (– 2, 2). Let this point be Z.
Distance from a Point to a Line on a Coordinate Plane Step 4 Use the Distance Formula to determine the distance between Z(– 2, 2) and V(1, 5). Distance formula Substitution Simplify. Answer:
Distance from a Point to a Line on a Coordinate Plane Step 4 Use the Distance Formula to determine the distance between Z(– 2, 2) and V(1, 5). Distance formula Substitution Simplify. Answer: The distance between the point and the line is or about 4. 24 units.
COORDINATE GEOMETRY Line n contains points (2, 4) and (– 4, – 2). Find the distance between line n and point B(3, 1). (2, 4) B(3, 1) (– 4, 2) A. B. C. D.
COORDINATE GEOMETRY Line n contains points (2, 4) and (– 4, – 2). Find the distance between line n and point B(3, 1). (2, 4) B(3, 1) (– 4, 2) A. B. C. D.
Distance Between Parallel Lines Find the distance between the parallel lines a and b whose equations are y = 2 x + 3 and y = 2 x – 1, respectively. You will need to solve a system of equations to find the endpoints of a segment that is perpendicular to both a and b. From their equations, we know that the slope of line a and line b is 2. Sketch line p through the y-intercept of line b, (0, – 1), perpendicular to lines a and b. a b p
Distance Between Parallel Lines Step 1 Write an equation for line p. The slope of p is the opposite reciprocal of Use the y-intercept of line b, (0, – 1), as one of the endpoints of the perpendicular segment. Point-slope form Simplify. Subtract 1 from each side.
Distance Between Parallel Lines Step 2 Use a system of equations to determine the point of intersection of the lines a and p. Substitute 2 x + 3 for y in the second equation. Group like terms on each side.
Distance Between Parallel Lines Simplify on each side. Multiply each side by Substitute equation for p. . for x in the
Distance Between Parallel Lines Simplify. The point of intersection is or (– 1. 6, – 0. 2).
Distance Between Parallel Lines Step 3 Use the Distance Formula to determine the distance between (0, – 1) and (– 1. 6, – 0. 2). Distance Formula x 2 = – 1. 6, x 1 = 0, y 2 = – 0. 2, y 1 = – 1 Answer:
Distance Between Parallel Lines Step 3 Use the Distance Formula to determine the distance between (0, – 1) and (– 1. 6, – 0. 2). Distance Formula x 2 = – 1. 6, x 1 = 0, y 2 = – 0. 2, y 1 = – 1 Answer: The distance between the lines is about 1. 79 units.
Find the distance between the parallel lines a and b whose equations are respectively. A. 2. 13 units B. 3. 16 units C. 2. 85 units D. 3 units and ,
Find the distance between the parallel lines a and b whose equations are respectively. A. 2. 13 units B. 3. 16 units C. 2. 85 units D. 3 units and ,
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