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

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript
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?
Document related concepts

Line (geometry) wikipedia, lookup

Euclidean geometry wikipedia, lookup

Pythagorean theorem wikipedia, lookup

Rational trigonometry wikipedia, lookup

Integer triangle wikipedia, lookup

Trigonometric functions wikipedia, lookup

Technical drawing wikipedia, lookup

Perspective (graphical) wikipedia, lookup

History of trigonometry wikipedia, lookup

Noether's theorem wikipedia, lookup

Golden ratio wikipedia, lookup

Riemannian connection on a surface wikipedia, lookup

Euler angles wikipedia, lookup

Reuleaux triangle wikipedia, lookup

Four color theorem wikipedia, lookup

Duality (projective geometry) wikipedia, lookup