1 2

3 4

5 6 7 8

b a a+b=______

b c

a

a+b+c=______

5.1 Interior angles of a polygon

Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorAngles 180

Sum of the interior angles of a n-sided Polygon = (n-2) 180D

What you need to know: How to use the formula 1) The sum of the measures of the interior angles of a 25-gon is ___________. How to find one angle in a regular polygon 2) The measure of one angle in a regular octagon is _________. How to use the formula in reverse 3) How many sides does a polygon have if the sum of its interior angles is 3060?_____________

Review

70 D

110D

5.2 Exterior angles of a polygon. 1. Sketch the exterior angles of the octagon 2. measure each exterior angle of each polygon 3. find the sum of all to the exterior angles of each polygon The sum of all exterior angles of a polygon add up to _________________. What you need to know. 1) The sum of the exterior angles is constant----The sum of the measures of the exterior angles of a 25-gon is _____________ 2) How to use the new knowledge backwards----If the measure of one exterior angle of a regular polygon is 24°, then the polygon has_____________ sides. 1. Find all of the missing angles.

Vertex Angle

Vertex Angle

NonVertex Angles

5.3 Kite and trapezoid properties 1. There are two sets of congruent Adjacent sides. 2. Diagonals are perpendicular. 3. The line connecting the vertex angles bisects the vertex angles and the other diagonal. 4. Two isosceles triangles are formed with a kite. ---The base angles are congruent. 5. Four right triangles are formed with a kite. 6. Nonvertex angles are congruent.

The following are kites.

1. x = _____ y = _____ 2. x = _____ y = _____

1 5 1 °

7 3 ° y

x

Isosceles Trapezoid BASE

LEG LEG BASE Diagonals are congruent Diagonals create 4 sets of congruent angles. 1. Bottom base angles are congruent. Top base angles are congruent. 2. Consecutive angles between the bases are supplementary. (any trapezoid)

3. Legs are congruent.

1. x = _____ y = _____ 2.Perimeter = 105 cm x = _____

1 2 1 ° y

x

3 0 c m

x

2 3 c m

Find the measures of every letter.

7 0 °

3 0 °

1 0 0 °

1 0 6 °

4 0 °

h b

a c

d

k j

m

r q

s t

v

u

f

e

n i

g

p

l 1

l 2

l 3 l 4

l 1 �� l 2 l 3 �� l 4

a= b= c= d= e= f= g= h= i= j= k= m= n= p= q= r= s= t= u= v=

Review 1. x = _____ y = _____

1 2 1 ° y

x

2. x = _____ y = _____ D80 y+3 x-20 3. x = _____ y = _____ 100 D y

60D

x 1. Draw a regular polygon. 2. Draw an equilateral polygon. 1. If the sum of the measures of two angles is 90°, then the angles are __________________. 2. In an isosceles triangle, the base angles are _________________. 3. The sum of the measures of the angles of an octagon is ________. 4. Each angle of a regular hexagon measures __________________. 5. The diagonals of a __________________ are perpendicular bisectors of each other.

5.4 Midsegments. A segment that connects any two midpoints of a triangle and the nonparallel sides of a trapezoid

properties of midsegments for triangles.

Use your ruler to show the following are true: 1. Each midsegment bisects the sides with the midpoints. 2. The midsegment is half the length of the third side. 3. The midsegment is parallel to the third side. 4. The three midsegments create four triangles. These triangles are ___________________. properties of midsegments for triangles. http://www.mathopenref.com/trapezoidmedian.html

Use your ruler and protractor to show the following are true: 1. The midsegment bisects the legs. 2. Half the sum of the lengths of the bases is equal to the length of the midsegment. 3. The midsegment is parallel to the bases. 4. The angle formed by the leg and base is congruent to the corresponding angle formed by the same leg and

midsegment.

1. Perimeter = 105 cm x = _____

3 0 c m

x

2 3 c m

2–3. Find the missing values in each figure. 2. x = ____ y = ____ z = ____

x

6 0 ° 4 0 °

z y

2 6

2 3 1 7

3. The figure is a trapezoid. q = _____

1 3

2 4

q 4. The midsegment of a trapezoid is _________________ to the two bases. 5. The length of a midsegment between two sides of a triangle is _______ the length of the third side. 6. The length of the midsegment of a trapezoid is ____________________________ of the lengths of the bases. 7. Draw one median in one triangle and one midsegment in the other triangle and label each as such.

xz y

z

D30

15

� �5,

� �qp,

5.5 Parallelograms. A quadrilateral where opposite sides are parallel. Use your ruler and protractor to show the following are true: 1. Opposite angles are congruent. 2. Consecutive angles are supplementary. 3. Opposite sides are equal in measure. 4. The diagonals of a parallelogram bisect each other. 5. The diagonals form two sets of vertical angles. 1. a = _____

b = _____ x = _____ y = _____

2. Find the missing coordinate in terms of p and q 8. The length of the midsegment of a trapezoid is the ____________ of the lengths of the bases. 9. The opposite angles of a parallelogram __________________. 10. The diagonals of a parallelogram __________________. 11. The consecutive angles of a parallelogram ________________.

5.6 Special parallelograms. Rhombus, Rectangle, and Square. Properties of a Rhombus (a square is a rhombus)

Use your ruler and protractor to show the following are true: 1. These are all parallelograms, so parallelogram rules above apply. 2. The diagonals are perpendicular to each other. 3. All sides are equal in length. 4. The diagonals bisect the angles. Properties of a Rectangle (a square is a rectangle) Use your ruler and protractor to show the following are true: 1. These are all parallelograms, so same rules apply. Apply them to the Rectangle. 2. The diagonals are not perpendicular to each other, but they do bisect each other. 3. The measure of each angle is the same. 4. The diagonals are equal in length.

55

x

y 41

D105 a

b 1. Lengths x= y= Angles a= b= Complete each statement. None of the answers is square. 1. If the sum of the measures of two angles is 90°, then the angles are __________________. 2. In an isosceles triangle, the base angles are _________________. 3. The sum of the measures of the angles of an octagon is _____________________. 4. Each angle of a regular hexagon measures _____________________. 5. The diagonals of a _________________________ are perpendicular bisectors of each other. 6. The midsegment of a trapezoid is _________________________ to the two bases. 7. The length of a __________________between two sides of a triangle is half the length of the third side. 8. The length of the midsegment of a trapezoid is ____________________the sum of the lengths of the bases. 9. The opposite angles of a parallelogram are __________________. 10. The diagonals of a parallelogram _____________________________________. 11. The consecutive angles of a parallelogram are ___________________________________. 12. The diagonals of a ___________________________________ bisect the opposite angles. 13. The diagonals of a _________________________________ are equal in length.

Given diagonal 𝐵𝐾 and ∠𝐵, construct rhombus BAKE.

B K

B