1. Brett Solberg – AHS – ’11-’12
4.3 & 4.4 Geometry
Brett Solberg – AHS – ’11-’12

2. Warm-up
Solve for a, b, and c. Justify your reasoning.
a b c
40° °

3. Today’s Objectives Parallel and Perpendicular Lines. Triangles
Relationships to each other.
Triangles
Triangle Sum Theorem
Classification
Exterior Angle Theorem

4. Fill In the Blanks Any friend of yours is… a friend of mine.
The enemy of my enemy is…
my friend.
The enemy of my friend is…
my enemy.
Friends = Lines that are parallel
Enemies = Lines that are perpendicular

5. Theorem 3.9 l m n If two lines are parallel to the same line, then
they are parallel to each other. l m n

6. Theorem 3.10 l m n If two lines are perpendicular to the same line,
then they are parallel to each other. l
m n

7. Theorem 3.11
If a line is perpendicular to one of two parallel lines,
then it is perpendicular to the other line. l
m n

8. Worksheet Example #6 How are a and e related?
a || b, b || c, c | d, d || e a b c
d e

9. Worksheet
You have 15 minutes to work on the worksheet.

10. Triangles
What is the sum of the angles in the triangle?
a b c
40° °

11. Triangle Angle Sum Theorem
The sum of the angles in any triangle is 180°.
80°
40° °
= 180

12. Triangle Classifications
Triangles are classified by their angles and the number of congruent sides.

13. Acute Triangle
Triangle where the measure of every angle is less than 90°.

14. Obtuse Triangle
Triangle where one angle measure is greater than 90°.

15. Right Triangle
Triangle with one angle measure equal to 90°.

16. Equiangular Triangle Triangle where all angles are congruent.
What would the measure of the angles be?

17. Scalene Triangle
Triangle where no side lengths are congruent.

18. Isosceles Triangle
Triangle where two side lengths are congruent.

19. Equilateral Triangle
Triangle where all three side lengths are congruent.

20. Classify the Triangles
By angles.

21. Classify the Triangles
By Side Lengths

22. Exterior Angle
An angle formed by the side of a triangle and the extension of the adjacent side.
Exterior Angle

23. Remote Interior Angles
The two angles inside the triangle which are not adjacent to the exterior angle.
Exterior Angle
Remote Interior Angles

24. Triangle Exterior Angle Theorem
The measure of the exterior angle is equal to the sum of the remote interior angles.
Exterior Angle
Remote Interior Angles
120
= 120

25. Example Find x, y, and z. 55 + 90 + x = 180 by Triangle Angle Sum Thm.
y = by Exterior Angles Thm.
10 + y + z = 180 by Triangle Angle Sum Thm.
x y z

26. Worksheet
Both worksheets are due by next class.