2. A Polygon is a simple closed figure formed by three or more straight lines.
Polygons
Not Polygons
A Regular Polygon is a polygon that has all sides congruent and all angles congruent.
Square
Equilateral Triangle

3. Types of Polygons
Heptagon
7 sides
Triangle
3 sides
Quadrilateral
4 sides
Octagon
8 sides
Pentagon
5 sides
Nonagon
9 sides
Hexagon
6 sides
Decagon
10 sides

4. Types of Quadrilaterals
Parallelogram - quadrilateral with opposite sides parallel & congruent
Rectangle - parallelogram with 4 right angles
Square - parallelogram with 4 right angles and 4 congruent sides
Rhombus - parallelogram with 4 congruent sides
Trapezoid - quadrilateral with one pair of parallel sides

5. mx = 110° Finding the angle measures in a polygon.
Find the missing angle measure in this quadrilateral.
110° X°
80°
60°
*The sum of the measures of the angles of a quadrilateral is equal to 360°
X = 360
250 + X = 360
– 250
– 250
X = 110
mx = 110°

6. mx = 125° Try This: Find the missing angle measure in this pentagon.
120°
75°
Find the missing angle measure in this pentagon. X°
120°
100°
Sum of angles = (n –2) x 180°
pentagon: n = 5 sides
(5 –2) x 180°
Sum of angles of pentagon = 540°
X = 540°
415 + X = 540
– 415
– 415
X = 125
mx = 125°

7. (n –2) x 180° = sum of angles (6 –2) x 180° = 4 x 180 = 720
Find the measure of an angle of a regular hexagon.
(n –2) x 180° = sum of angles
Regular Hexagon
(6 –2) x 180° = 4 x 180 = 720
The sum of the angles of a hexagon is 720°.
There are 6 congruent angles in a regular hexagon.
720° ÷ 6 = 120°
The measure of an angle of a regular hexagon is 120°.

8. corresponding angles of similar figures are congruent
Similar figures have the same shape but not necessarily the same size. D E F
ABC ~ DEF A B C n o m x y z
corresponding angles of similar figures are congruent
A  D;
B  E;
C  F
corresponding sides of similar figures are proportional

9. Determine whether each pair of figures is similar.
55° D
55° ?
35°
35° ? E F I H
Find the missing angle measure for each triangle.
180 – 125 = 55,
m E = 90°,
= 125,
m D = 55°
180 – 145 = 35,
m I = 35°
m H = 90°,
= 145,
Corresponding angles of similar figures are congruent
The corresponding angles are congruent, so the triangles are similar.
DEF~ GHI

10. Determine whether each pair of figures is similar.B C
12m
16m
18m
24m
Write a proportion. Use cross products to show that the ratios are equal and form a true proportion.
12 • 24 = 18 • 16
288 = 288
corresponding sides of similar figures are proportional
The corresponding sides are proportional, so the triangles are similar.
ABC~ DEF

11. Find the missing side measure of similar triangles.B C 4m 6m
12m 9m 6m
ABC ~ DEF ?
Write a proportion. Use cross products to find the missing part. AB BC
Substitute measures of sides. =
Let n = measure of EF ED EF
4 • n = 6 • 12
4 n = 72 4 4
The measure of EF is 18m.
n = 18

12. Find the missing side measure of similar triangles.
Try This:
Find the missing side measure of similar triangles. G D
DEF ~ GHI 6m 8m E F
12m I n H ?
Write a proportion. Use cross products to find the missing part.
Let n = measure of EF
6 ∙ n = 12 ∙ 8
6 n = 96 6 6
The measure of IH is 16m.
n = 16

13. Joe wants to resize a picture that is 4 inches wide by 6 inches long to make a poster that is 30 inches long to fit on his wall. What will be the width of the poster?
Write a proportion. Use cross products to find the missing part.
6 in 6 4 = n 30
4 in
6 ∙ n = 4 ∙ 30
6 n = 120 6 6
30 in
n = 20 in
The width of the poster will be 20 inches.
20 in ?