Tyiana Combs Geo 1
Objective
~ To use a transversal in proving parallel lines
Vocabulary
Flow Proof ~ a proof is a convincing argument that uses deductive reasoning.
A form of a proof is a flow proof in which arrows show the logical
connections between the statements.
Example of a Flow Proof (for the HL Theorem)
Postulate 3-2 Converse of the Corresponding Angles Postulate
If two lines and a transversal form corresponding angles that are congruent, then the two lines
are parallel.
Theorem 3-5 Converse of the Alternative Interior Angles Theorem
If two lines and a transversal form alternate interior angles that are congruent, then the two
lines are parallel. If angle 1 is congruent to angle 2, then l is parallel to m.
Theorem 3-5 Converse of the Alternative Interior Angles Theorem
If two lines
a transversal
alternate
interiorAngles
angles Theorem
that are congruent, then the two
Theorem
3-6 and
Converse
of the form
Same-Side
Interior
are parallel.
If angle 1 isform
congruent
to angle
2, then
l is parallel
m.
If lines
two lines
and a transversal
same-side
interior
angles
that aretosupplementary,
then the
two lines are parallel. If angle 4 is congruent to angle 5, then l is parallel to m.
Theorem 3-7 Converse of the Alternative Exterior Angles Theorem
If two lines and a transversal form alternate exterior angles that are congruent, then the two
lines are parallel. If angle 1 is congruent to angle 7, then l is parallel to m.
Theorem 3-8 Converse of the Same-Side Exterior Angles Theorem
If two lines and a transversal form same-side exterior angles that are supplementary, then the
two lines are parallel. If angle 1 is congruent to angle 4, then l is parallel to m.
1. Make a proof for Theorem 3-5. Given: Angle 1 is congruent to Angle 2. Prove: l is parallel
to m.
2. Which lines, if any (using the diagram shown in Theorem 3-6), must be parallel if Angle 1
is congruent to Angle 5?
3. Find the value of x for which l is parallel to m.
40•
(2x+6)
4. Which lines or segments are parallel? Justify your answer.
C
B
E
G
5. Fill in the blanks and name the theorem:
If two lines and a transversal form same-side __________ angles that are _______________,
then the two lines are _________. If angle 4 is congruent to angle 5, then l is parallel to m.
1. Theorem 3-5
Statements
Reasons
Angle 1 is congruent Given
to Angle 2
Angle 1 is congruent Vertical angles are congruent
to Angle 3
Angle 3 is congruent Transitive Property of Congruence
to Angle 2
l is parallel to m
Corresponding angles are congruent
2. Line l and Line m.
3.
2x + 6 = 40
2x = 34
Subtract 6 from each side.
x = 17
Divide each side by 2.
4. Line BE is parallel to Line CG using the Converse of Corresponding Angles Postulate.
5. Converse of the Same-Side Interior Angles Theorem
If two lines and a transversal form same-side interior angles that are supplementary, then the
two lines are parallel. If angle 4 is congruent to angle 5, then l is parallel to m.