Geometry Notes

Sections 2-8

What you’ll learn

How to write proofs involving supplementary and complementary angles

How to write proofs involving congruent and right angles

Vocabulary There is no new vocabulary However. . . Do you know these definitions. . .?

Supplementary AnglesComplementary AnglesReflexive PropertySymmetric PropertyTransitive PropertyPerpendicular linesLinear Pair of AnglesVertical AnglesCongruent Angles

Adjacent AnglesCongruent Segments Angle Addition PostulateSegment Addition PostulateMidpointSegment BisectorAngle BisectorOpposite Rays I hope so. . . .

Congruence of Segments is . . .

Reflexive segments

Symmetric segments

Transitive segments

A segment is congruent to itself.

AB AB

You can switch the left and right sides

If AB CD then CD AB.

If AB CD and CD EF, then AB EF.

Congruence of Angles is . . .

Reflexive angles

Symmetric angles

Transitive angles

An angle is congruent to itself.

A A

You can switch the left and right sides

If A B then B A.

If A B and B C, then A C.

Supplement Theorem

What are we given?Look in the hypothesis of the conditional statement and draw it.

Now what can we conclude?Look in the conclusion of the conditional statement 1 and 2 are supplementary.

If two angles form a linear pair,

then they are supplementary.

two angles form a linear pair, 1

2

they are supplementary

How does this work in problems?

Linear pairs → supplementary → add up to 180

12

If 1 and 2 form a linear pair and m2 = 67, find m1.

More example problems

Linear pairs → supplementary → add up to 180

Find the measure of each angle.

More example problems

Linear pairs → supplementary → add up to 180

Find the measure of each angle.

Vertical Angles We’ve done this before.

Draw two vertical angles If two angles are vertical angles then they

are congruent.

Vert. s → → =

How does this work in problems?

1 2

If m2 = 72, find m1.

Vert. s → → =

More example problems

Find the measure of each angle.

Vert. s → → =

More theorems. . . Complement theorem If the noncommon sides of two adjacent angles

form a right angle, then the angles are complementary angles.

1

2

1 & 2 complementary → m 1 + m 2 = 90

More theorems. . . Angles supplementary to the same angle

or to two congruent angles are congruent.

More theorems. . . Angles complementary to the same angle

or to two congruent angles are congruent.

More theorems. . . Perpendicular lines intersect to form four

right angles. All right angles are congruent. Perpendicular lines form congruent

adjacent angles. If two angles are congruent and

supplementary, then each angle is a right angle.

If two congruent angles form a linear pair, then they are right angles.

Have you learned .. . .

How to write proofs involving supplementary and complementary angles?

How to write proofs involving congruent and right angles?

Assignment: Worksheet 2.8A