Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Definitions Parallel Lines Two...

DefinitionsParallel LinesTwo lines are parallel lines if they lie in the same plane and do not intersect.

DefinitionsPerpendicular LinesTwo lines are perpendicular lines if they intersect to form a right angle.

DefinitionsSkew LinesTwo lines are skew lines if they do not lie in the same plane. Skew lines never intersect.

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.

Theorem 3.1All right angles are congruent.

Theorem 3.2• If two lines are perpendicular, then

they intersect to form four right angles.

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.

Theorem 3.4If two sides of adjacent acute angles are perpendicular, then the angles are complementary.

Section 3.4 & 3.5 Parallel lines and Transversals

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

DefinitionsAlternate Interior AnglesAre two nonadjacent interior angles that lie on opposite sides of a transversal

DefinitionsAlternate Exterior Angles Are two nonadjacent exterior angles that lie on opposite sides of a transversal

Definitions

Same-Side Interior Angles Are interior angles that lie on the same side of a transversal

DefinitionsCorresponding Angles Are two nonadjacent angles, one interior and one exterior, that lie on the same side of a transversal

1) Identify pairs of angles.

Corresponding angles

Alternate interior angles

Same-side interior angles

Alternate exterior angles

Theorems, Postulates, & DefinitionsCorresponding Angles Postulate 8: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

corresponding angles

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

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

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

Theorem 3.12In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

2) Find angle measures formed by parallel lines

and transversals.

m || n and m1 = 135°.

3) Given m || n and transversal t

Prove: 1 3

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Definitions Parallel Lines Two...

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