1. Page 248 #1-9 ANSWERS

2. Pre-Algebra Homework
Page 248 #10-15

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

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

5. 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)

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

8. 5-4 Polygons Warm Up Problem of the Day Lesson Presentation
Pre-Algebra

9. Vocabulary polygon regular polygon trapezoid parallelogram rectangle
rhombus
square

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

12. 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°

13. 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°

14. 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°

15. 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°

16. 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.

17. 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°

18. 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°

19. 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°

20. 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°

21. 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

22. 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

23. 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

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

25. GRAPH PAPER RECOMMENDED!

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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