Download Parallel and Perpendicular Lines

Geometry – Chapter 3
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2.0 Students write geometric proofs
4.0 Students prove basic theorems involving
congruence
7.0 Students prove and use theorems
involving the properties of parallel lines cut
by a transversal
12.0 Students find and use measures of
interior and exterior angles of triangles and
polygons to classify figures and solve
problems.
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a transversal is a line that intersects two
coplanar lines at two distinct points.
the diagram shows the eight angles formed
by a transversal t and two lines, l and m.
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There are special names for certain angles in
a 2 line and transversal relationship
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alternate interior angles
same-side interior angles
corresponding angles
alternate exterior angles
same-side exterior angles
Draw a transversal using a ruler through your
not-parallel lines. Discuss which angles you
think are which and why.
◦ alternate interior angles
◦ same-side interior angles
◦ corresponding angles
◦ alternate exterior angles
◦ same-side exterior angles
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Draw a transversal using a ruler through your
parallel lines. Use a protractor to measure all
of the angles. Discuss and draw conclusions
about angle relationships when the two lines
are parallel.
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alternate interior angles
same-side interior angles
corresponding angles
alternate exterior angles
same-side exterior angles
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Homework: page 132 (1-16) all
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What is the Corresponding Angles Postulate?
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What is the converse to this?
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Everything goes back to either the
Corresponding Angles Theorem or the
Converse of the Corresponding Angles
Theorem.
When you begin a proof involving parallel
lines, you should ask yourself “How do I show
that corresponding angles are congruent?”
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What is the converse to the Alternate Interior
Angles Theorem?
If two lines and a transversal form alternate
interior angles that are congruent, then the
two lines are parallel.
Proof:
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What is the converse to 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.
Proof:
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State the Converse to the Alternate Exterior
Angle Theorem
If two lines and a transversal form alternate
interior angles that are congruent, then the
two lines are parallel.
Proof:
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State the Converse to the Same-side Exterior
Angle Theorem
If two lines and a transversal form same-side
interior angles that are supplementary, then
the two lines are parallel.
Proof:
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Homework:
page 137 (1-21) all
page 143 (1-3)
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5.
In this drawing, line k is parallel to line j
Which angle is alternate interior with ∠4?
Which angle is corresponding to ∠8?
m∠3 = 37. What is m∠6?
m∠1 = x+12 and m∠5 = 3x – 36. What is x?
Given that k∥j, write a proof to show that ∠2 and
∠5 are supplementary.
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homework:
page 150 (1-6, 10-20) all
page 161 (1-21) all