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DefinitionsParallel LinesTwo lines are parallel lines if they lie in the same plane and do not intersect.
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DefinitionsPerpendicular LinesTwo lines are perpendicular lines if they intersect to form a right angle.
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DefinitionsSkew LinesTwo lines are skew lines if they do not lie in the same plane. Skew lines never intersect.
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DefinitionsConverseThe converse of an if-then statement is the statement formed by switching the hypothesis and the conclusion. Here is an example.
Statement: If two segments are congruent, then the two segments have the same length.
Converse: If two segments have the same length, then the two segments are congruent.
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Theorem 3.1All right angles are congruent.
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Theorem 3.2• If two lines are perpendicular, then
they intersect to form four right angles.
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Theorem 3.3If two lines intersect to form adjacent congruent angles, then the lines are perpendicular.
Converse:If two lines are perpendicular, then they form congruent adjacent angles.
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Theorem 3.4If two sides of adjacent acute angles are perpendicular, then the angles are complementary.
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Section 3.4 & 3.5 Parallel lines and Transversals
3.3 Parallel Lines and Transversals
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3.3 Parallel Lines and Transversals
DefinitionsTransversal:Is a line, ray or segment that intersects two or more coplanar lines, rays or segments each at a different point
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3.3 Parallel Lines and Transversals
DefinitionsAlternate Interior AnglesAre two nonadjacent interior angles that lie on opposite sides of a transversal
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3.3 Parallel Lines and Transversals
DefinitionsAlternate Exterior Angles Are two nonadjacent exterior angles that lie on opposite sides of a transversal
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3.3 Parallel Lines and Transversals
Definitions
Same-Side Interior Angles Are interior angles that lie on the same side of a transversal
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3.3 Parallel Lines and Transversals
DefinitionsCorresponding Angles Are two nonadjacent angles, one interior and one exterior, that lie on the same side of a transversal
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3.3 Parallel Lines and Transversals
1) Identify pairs of angles.
Corresponding angles
Alternate interior angles
Same-side interior angles
Alternate exterior angles
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3.3 Parallel Lines and Transversals
Theorems, Postulates, & DefinitionsCorresponding Angles Postulate 8: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
.
corresponding angles
2 3
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3.3 Parallel Lines and Transversals
Theorems, Postulates, & DefinitionsAlternate Interior Angles Theorem 3.3.3: If two lines cut by a transversal are parallel, then alternate interior angles are congruent.alternate interior angles
1 3
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3.3 Parallel Lines and Transversals
Theorems, Postulates, & DefinitionsAlternate Exterior Angles Theorem 3.3.4: If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.alternate exterior angles
2 5
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3.3 Parallel Lines and Transversals
Theorems, Postulates, & Definitions
Same-Side Interior Angles Theorem 3.3.5: If two lines cut by a transversal are parallel, then same-side interior angles are supplementary.same-side interior angles
1 + 4 = 180
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Theorem 3.12In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
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3.3 Parallel Lines and Transversals
2) Find angle measures formed by parallel lines
and transversals.
m || n and m1 = 135°.
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3.3 Parallel Lines and Transversals
3) Given m || n and transversal t
Prove: 1 3
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