Download 3.4: Parallel and Perpendicular Lines 3.5: Parallel Lines and Triangles

3.4: Parallel and Perpendicular Lines
Theorem: If two lines are parallel to the same line, then they are parallel to each other.
Theorem: In a plane, if two lines are perpendicular to the same transversal, then the two lines are parallel to each other.
Theorem: In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
a ll b and a t
a
b
t
3.5: Parallel Lines and Triangles
Triangle: A figure formed by three segments joining three noncollinear points.
B
Triangle ABC ( ABC)
Vertices of C
A
Sides of Angles of
Classify Triangles by the number of congruent sides
Classify Triangles by their angles
Auxiliary Line: A line added to a diagram to help in a proof.
Triangle Sum Theorem
Example:
The sum of the measure of the angles of a triangle is 180.
Find the value of x. Then give the measure of each angle.
The measure of on angle of a triangle is 5 more than the measure of the smallest angle. The measure of the third angle is three times the measure of the smallest angle. What are the measures of the 3 angles?
Use the given information to ind the unknown angle measures in the triangle.
100
53
12
w
x
2x + y
y
5x + ­ y
5x The perimeter of my triangle is 60 ft. The sides are in the ratio 3:4:5. What are the sides of my triangle?