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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Complete each sentence. 1 . Two lines in a plane that never meet are called lines. 2 . lines intersect at right angles. 3 . The symbol || means that lines are .

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Complete each sentence. 1. Two lines in a plane that never meet are called lines. 2. lines intersect at right angles. 3. The symbol || means that lines are . 4. When a transversal intersects two lines, all of the acute angles are congruent. parallel Perpendicular parallel parallel

  3. California Standards MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. Also covered:AF3.3

  4. Vocabulary polygon quadrilateral trapezoid parallelogram rectangle rhombus square

  5. In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

  6. 3 2 slope of EF = 3 5 slope of GH = 3 5 slope of PQ = –2 3 2 3 slope of CD = or – 3 –3 slope of QR = or –1 Additional Example 1: Finding Perpendicular and Parallel Lines Which lines are parallel? Which lines are perpendicular? Step 1 Find the slope of each line.

  7. GH || PQ 3 5 3 5 The slopes are equal. = EFCD The slopes have a product of –1: • – = –1 2 3 3 2 Additional Example 1 Continued Which lines are parallel? Which lines are perpendicular? Step 2 Compare the slopes.

  8. –4 6 –6 4 –2 3 –3 2 slope of AB = or slope of EF = or –2 3 slope of CD = 2 3 slope of GH = 3 3 slope of JK = or 1 Check It Out! Example 1 Which lines are parallel? Which lines are perpendicular? Step 1 Find the slope of each line. A C K D E H B J G F

  9. GHAB CD || EF –2 3 –2 3 The slopes are equal. = The slopes have a product of –1: • – = –1 3 2 2 3 Check It Out! Example 1 Continued Which lines are parallel? Which lines are perpendicular? Step 2 Compare the slopes. A C K D E H B J G F

  10. A polygon is a closed plane figure formed by three or more line segments called sides. Each side meets exactly two other sides, one on each end, in a common endpoint. Quadrilaterals are polygons with four sides and four angles. Quadrilaterals with certain properties are given additional names.

  11. CD || BA and BC || AD Additional Example 2: Using Coordinates to Classify Quadrilaterals Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral. A(3, –2), B(2, –1), C(4, 3), D(5, 2) parallelogram

  12. TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Check It Out! Example 2 Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) 2 pairs of parallel sides, 4 right angles. parallelogram, rectangle, rhombus, square

  13. Additional Example 3: Finding the Coordinates of a Missing Vertex Find the coordinates of the missing vertex. Rectangle WXYZ with W(–2, 2), X(3, 2), and Y(3, –4) Step 1 Graph and connect the given points. W X Step 2 Complete the figure to find the missing vertex. The coordinates of Z are (–2, –4). Y Z

  14. Check It Out! Example 3 Find the coordinates of the missing vertex. Rectangle JKLM with J(–1, 2), K(4, 2), and L(4, –1) Step 1 Graph and connect the given points. J K Step 2 Complete the figure to find the missing vertex. L M The coordinates of M are (–1, –1).

  15. 10 3 – MN, RQ Lesson Quiz Determine the slope of each line. 1.PQ 2.MN 3.MQ 4.NP 5. Which pair of lines are parallel? 1 8 7

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