Post on 17-Dec-2015
Transversals and Angles 3-4A
What is a transversal?
What are four types of angles made by a transversal?
What are the five steps in a deductive proof?
DefinitionA transversal is a line that intersects two
coplanar lines at two different points.
Exterior
Exterior
Interior
12
34
5 6
78
r
s
Transversal t
Angles formed by Transversals
Alternate interior angles
6&4 5&3
1 2
34
5 6
78
interior
Angles formed by Transversals
Alternate exterior angles
7&1
1 2
34
5 6
78
8&2
exterior
exterior
Angles formed by Transversals
Same-side interior angles
5&4
1 2
34
5 6
78
6&3
interior
Angles formed by Transversals
Corresponding angles
5&1
1 2
34
5 6
78
6&2 7&3 8&4
Try ItName:
The transversal
Two pairs of same side interior
Two pairs of alternate exterior angles
Two pairs of alternate interior angles
Four pairs of corresponding angles
1 2 3 45678
p q
r
Five Step Deductive Proof
1. Rewrite the conjecture to be proved in if-then form.
2. Draw and label a figure to represent the given information.
3. State the statement to be proved in terms of the figure.
4. Plan the proof. Find a logical sequence of steps.
5. Demonstrate the argument by putting your plan into writing justifying every statement.
Do the rewrite, draw, and state stepsAll vertical angles are congruent.
Rewrite: If two angles are vertical angles, then they are congruent.
Draw: two angles are vertical angles
angles.verticalareand CBDABE
A
B
C
DE
State: Given:
Prove: CBDABE
• What is a transversal?
A transversal is a line that intersects two coplanar lines at two different points.
• What are four types of angles made by a transversal?
Alternate interior angles, alternate exterior angles, same-side interior angles and corresponding angles.
What are the five steps in a deductive proof?
1. Rewrite the conjecture to be proved in if-then form.
2. Draw and label a figure to represent the given information.
3. State the statement to be proved in terms of the figure.
4. Plan the proof. Find a logical sequence of steps.
5. Demonstrate the argument by putting your plan into writing justifying every statement.
Assignment
Page 219, 1-5,
9-10, 19-23.