3-1



..Angles of a Triangle

3-4

(A) A triangle is a figure formed by 3 __________ joining 3 ______________ ___________

Draw a picture and describe each of the following triangles.

1. Scalene 4. Acute

2. Isoceles 5. Obtuse

3. Equilateral 6. Right

(B) Given triangle ABC. Draw a line throught B that is parallel to segment AC.

Show algebraically how the sum of the angles of the triangle equal 180 degrees.

EX. (1) Find x (2) Find x

(3) Find a What must be true about angle in a right triangle?

(4) Find x and y Conclusion?

(C) Show algebraically the relationship between the exterior angle BCD and angles A and B.

Ex:

(1) Find x and y (2) Find x

(3) Find x and y

(a) (b)

(c) (d)

(e) Find ? (f) Find x, y, z

(g)

Proofs

. [pic]

Given: a((b, c((d

Prove: (1 ( (7

.

3-5

The sum of the measures of the angles of a convex polygon with n sides

is _______________________________

The sum of the measures of the exterior angles of any polygon, one angle at

each vertex, is ___________.

What if the polygon is a regular polygon? What do you know about the angles?

Int angles = _______________

Ext angles = ______________

EXAMPLES

Find the interior sum, exterior sum, interior and exterior angles for each regular polygon with n sides.

(1)

|Number of sides (n) |6 |10 |24 |

|Interior sum | | | |

|Exterior sum | | | |

|Interior angle | | | |

|Exterior angle | | | |

Which is easier to find, an interior angle or an exterior angle?

2) An interior angle of a regular polygon = 160. How many side does it have?

3) Fill in the blanks

|number of sides | |9 | | |15 | | |

|ext angle | | |6 | | |8 | |

|interior angle | | | |165 | | |178 |

Review Questions

[pic]

Find:

m(FHD = ________ m(GHB = ________ m(HDE = ________

m(AHG = ________ m(BHC = ________ m(HDC = ________

m(FHG= ________ m(DHC = ________ m(HCD = ________

[pic]

Find:

m(1 = ________ m(2 = ________ m(3 = ________

m(4 = ________ m(5 = ________ m(6 = ________

3) Find the sum of the measures of the marked angles.

Sum = ___________________

4) Find the measure of each interior angle of a regular 25-gon.

_______________

Review Cont.

5. If a polygon has 11 sides, find the sum of the interior angles.

6. If a regular polygon has 36 sides, find each interior angle.

7. If 7 exterior angles of an octagon each measure 42, what is the measure of the 8th angle?

8. The second angle of a triangle is three times the first, and the third angle is nine less than

five times the first. Find the measure of each angle of the triangle.

9. a) if m(g = 81, m(e = 72, then m(i = ________.

b) if m(g = 46, m(i = 79, then m(h = _________.

10. For regular polygons, fill in the following chart completely.

|Number of sides |4 | | | |

|Each Interior ( | |171 | |170 |

|Each Exterior ( | | |3 | |

Solve for the variable(s) in each drawing.

11. 12.

13. 14.

15A. *15B..

x = ______ y = _____ z = _____ x = _____ y = ______

Proofs:

16. Given: m(ABD = m(AED

Prove: m(C = m(F

17. Given: [pic], (R ((T

Prove[pic]:

18. Given: m (( n; (1 ( (3

Prove: a (( b

19. Given [pic], [pic]

Prove: (1 ( (3

20. 21.

Given: [pic], [pic] Given: ................
................

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