Transversals and Angles 3-4A

1
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?

2
Definition

• A transversal is a line that intersects two
  coplanar lines at two different points.

Transversal t
Exterior
1
2
3
4
r
Interior
5
6
s
8
Exterior
7
3
Angles formed by Transversals
interior
1
2
4
3
5
6
7
8

• Alternate interior angles

4
Angles formed by Transversals
1
2
7
8

• Alternate exterior angles

5
Angles formed by Transversals
1
2
4
3
interior
5
6
7
8

• Same-side interior angles

6
Angles formed by Transversals
1
2
4
3
5
6
7
8

• Corresponding angles

7
Try It

• Name
• 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

8
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.

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Do the rewrite, draw, and state steps

• All vertical angles are congruent.
• Rewrite If two angles are vertical angles, then
  they are congruent.
• Draw two angles are vertical angles

A
C
D
E
B
State Given Prove
10

• 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.

11

• What are the five steps in a deductive proof?
• Rewrite the conjecture to be proved in if-then
  form.
• Draw and label a figure to represent the given
  information.
• State the statement to be proved in terms of the
  figure.
• Plan the proof. Find a logical sequence of
  steps.
• Demonstrate the argument by putting your plan
  into writing justifying every statement.

12
Assignment

• Page 219, 1-5,
• 9-10, 19-23.