Page 248 #1-9 ANSWERS

Pre-Algebra Homework Page 248 #10-15

Student Learning Goal Chart Lesson Reflection for Chapter 5 Sections 4 & 5

Pre-Algebra Learning Goal Students will understand plane geometry through plane figures and patterns in geometry.

Students will understand plane geometry through plane figures and patterns in geometry by completing the following: Learn to classify and name figures (5-1) Learn to identify parallel and perpendicular lines and the angles formed by a transversal (5-2) Learn to find unknown angles in triangles (5-3) Learn to classify and find angles in polygons. (5-4) Learn to identify polygons in the coordinate plane. (5-5)

Learning Goal Assignment Learn to classify and find angles in polygons.

5-4 Polygons Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Vocabulary polygon regular polygon trapezoid parallelogram rectangle rhombus square

Polygon Number of Sides 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon n n-gon

Additional Example 1A: Finding Sums of the Angle Measures in Polygons A. Find the sum of the angle measures in a hexagon. Divide the figure into triangles. 4 triangles 4 • 180° = 720°

Try This: Example 1A A. Find the sum of the angle measures in a hexagon. Divide the figure into triangles. 4 triangles 4 • 180° = 720°

Additional Example 1B: Finding Sums of the Angle Measures in Polygons Continued B. Find the sum of the angle measures in a octagon. Divide the figure into triangles. 6 triangles 6 • 180° = 1080°

Try This: Example 1B B. Find the sum of the angle measures in a heptagon. Divide the figure into triangles. 5 triangles 5 • 180° = 900°

The pattern is that the number of triangles is always 2 less than the number of sides. So an n-gon can be divided into n – 2 triangles. The sum of the angle measures of any n-gon is 180°(n – 2). All the sides and angles of a regular polygon have equal measures.

Additional Example 2A: Finding the Measure of Each Angle in a Regular Polygon Find the angle measures in the regular polygon. 6 congruent angles 6x = 180°(6 – 2) 6x = 180°(4) 6x = 720° 6x 6 720°6 = x = 120°

Find the angle measures in the regular polygon. Try This: Example 2A Find the angle measures in the regular polygon. 5 congruent angles 5a = 180°(5 – 2) a° 5a = 180°(3) a° a° 5a = 540° 5a 5 540° = a° a° a = 108°

Additional Example 2B: Finding the Measure of Each Angle in a Regular Polygon Find the angle measures in the regular polygon. 4 congruent angles 4y = 180°(4 – 2) 4y = 180°(2) 4y = 360° 4y 4 360°4 = y = 90°

Find the angle measures in the regular polygon. Try This: Example 2B Find the angle measures in the regular polygon. 8 congruent angles b° 8b = 180°(8 – 2) 8b = 180°(6) 8b = 1080° 8b 8 1080° = b = 135°

Additional Example 3A: Classifying Quadrilaterals Give all the names that apply to the figure. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rectangle 4 right angles rhombus 4 congruent sides square 4 congruent sides and 4 right angles

Additional Example 3B: Classifying Quadrilaterals Continued Give all the names that apply to the figure. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rhombus 4 congruent sides

Try This: Example 3A Give all the names that apply to the figure. A. quadrilateral Four-sided polygon parallelogram 2 pairs of parallel sides rectangle 4 right angles

Try This: Example 3B Give all the names that apply to the figure. B. quadrilateral Four-sided polygon

GRAPH PAPER RECOMMENDED!

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

parallelogram Try This: Example 3A Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) B CD || BA and BC || AD C A D parallelogram

Additional Example 3B: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU parallelogram, rectangle, rhombus, square

trapezoid Try This: Example 3B Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. E(1, 5), F(7, 5), G(6, 1), H(2, 1) EF || HG E F trapezoid H G

Additional Example 3C: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. G(1, –1), H(1, –2), I(3, –3), J(3, 1) GH || JI trapezoid

parallelogram, rectangle, rhombus, square Try This: Example 3C Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4) W ZW || YX and WX || ZY WX^ZW, XY^WX, YZ^XY and ZW^YZ Z X parallelogram, rectangle, rhombus, square Y

Additional Example 3D: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0) WZ || XY and WX || ZY WZ^ZY, ZY^XY, XY^WX and WX^WZ parallelogram, rectangle

parallelogram, rectangle Try This: Example 3D Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1) S TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU T R parallelogram, rectangle U