Properties and Theorems

List of Theorems

Chapters 1-3• Ruler Postulate• Segment Addition Postulate• Protractor Postulate• Angle Addition Postulate• Law of Detachment• Law of Syllogism• Addition Property of Equality• Subtraction Property of Equality• Multiplication Property of Equality• Division Property of Equality• Reflexive Property• Transitive Property• Substitution Property

• Right Angle Congruence Theorem• Congruent Supplements Theorem• Congruent Complements Theorem• Linear Pair Postulate• Vertical Angles Theorem• Parallel Postulate• Perpendicular Postulate• Corresponding Angles Postulate &

Converse• Alternate Interior Angles Theorem &

Converse• Consecutive Interior Angles Theorem &

Converse• Alternate Exterior Angles Theorem &

Converse

List of Theorems

Chapter 4• Triangle Sum Theorem• Exterior Angle Theorem• Third Angles Theorem• SSS Congruence Postulate• SAS Congruence Postulate• ASA Congruence Postulate• AAS Congruence Postulate• Base Angles Theorem• Base Angles Converse• Hypotenuse-Leg Congruence

Theorem

Chapter 5• Perpendicular Bisector Theorem &

Converse• Angle Bisector Theorem & Converse• Concurrency of Perpendicular Bisectors

of a Triangle• Concurrency of Angle Bisectors of a

Triangle• Concurrency of Medians of a Triangle• Concurrency of Altitudes of a Triangle• Midsegment Theorem• Exterior Angle Inequality• Triangle Inequality• Hinge Theorem• Converse of Hinge Theorem

4.1 – Triangles and Angles

Types of Triangles

Types of Triangles

Right and Isosceles Triangles

Interior vs. Exterior Angles

Triangle Sum Theorem

Exterior Angle Theorem

Corollary to the Triangle Sum Theorem

Classify the triangle by its angles and by its sides.

Classify the triangle by its angles and by its sides.

Classify the triangle by its angles and by its sides.

Complete the sentence with always, sometimes, or never.

Sketch the following triangles, if possible. If not possible, state so.

1. A right isosceles triangle2. An obtuse scalene triangle3. An acute equilateral triangle 4. A right obtuse triangle

Find the measure of the numbered angles.

Find the measure of the numbered angles.

Find the measure of the exterior angle shown

80 ( ) 180

3 22 180

80 3 22

80 2 22

102 2

51

51

x y

x y

x x

x

x

x

x

Realize this last problem is an example of the Exterior Angle Theorem

Find the measure of the exterior angle shown

2 3 51 4 8

2 54 4 8

54 2 8

46 2

23

23

4(23) 8 92 8 100

x x

x x

x

x

x

x

42

2 8

2(42 ) 8

84 8

76

m A

m B m A

m B

m B

m B

180

42 76 180

118 180

62

m A m B m C

m C

m C

m C

180

180 62

118

Exterior Angle C m C

Homework

• pp 198-199 1-28 all, 31-39 all, 47,49-50