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Theorem 2-3

Congruent Complements Theorem

If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. (p. 123)

• Proof on p. 125, Exercise 13

Theorem 2-4

All right angles are congruent. (p. 123)

• Proof on p. 125, Exercise 18

Theorem 2-5

If two angles are congruent and supplementary, then each is a right angle. (p. 123)

• Proof on p. 126, Exercise 23

Chapter 3 Parallel and Perpendicular Lines

Postulate 3-1

Corresponding Angles Postulate

If a transversal intersects two parallel lines, then corresponding angles are congruent. (p. 148)

Theorem 3-1

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent. (p. 149)

• Proof on p. 150

Theorem 3-2

Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then same-side interior angles are supplementary. (p. 149)

• Proof on p. 155, Exercise 25

Theorem 3-3

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent. (p. 151)

• Proof on p. 150, Got It 2

Postulate 3-2

Converse of the Corresponding Angles Postulate

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel. (p. 156)

Theorem 3-4

Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. (p. 157)

• Proof on p. 158

Theorem 3-5

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. (p. 157)

• Proof on p. 161, Exercise 29

Theorem 3-6

Converse of the Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel. (p. 157)

• Proof on p. 158, Problem 2

Theorem 3-7

If two lines are parallel to the same line, then they are parallel to each other. (p. 164)

• Proof on p. 167, Exercise 7

Theorem 3-8

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. (p. 165)

• Proof on p. 165

Theorem 3-9

Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. (p. 166)

• Proof on p. 168, Exercise 10

Postulate 3-3

Parallel Postulate

Through a point not on a line, there is one and only one line parallel to the given line. (p. 171)

Theorem 3-10

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180. (p. 172)

• Proof on p. 172

Theorem 3-11

Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. (p. 173)

• Proof on p. 177, Exercise 33
  • Corollary

    The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles. (p. 325)

    • Proof on p. 325

Spherical Geometry Parallel Postulate

Through a point not on a line, there is no line parallel to the given line. (p. 179)

Postulate 3-4

Perpendicular Postulate

Through a point not on a line, there is one and only one line perpendicular to the given line. (p. 184)

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