properties and theorems
DESCRIPTION
Properties and Theorems. List of Theorems. Chapters 1-3. Right Angle Congruence Theorem Congruent Supplements Theorem Congruent Complements Theorem Linear Pair Postulate Vertical Angles Theorem Parallel Postulate Perpendicular Postulate Corresponding Angles Postulate & Converse - PowerPoint PPT PresentationTRANSCRIPT
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 ( ) 1803 22 18080 3 22
80 2 22102 25151
x yx yx x
xx
xx
Realize this last problem is an example of the Exterior Angle Theorem
Find the measure of the exterior angle shown
2 3 51 4 82 54 4 854 2 846 22323
4(23) 8 92 8 100
x xx x
xxx
x
422 8
2(42 ) 884 8
76
m Am B m A
m Bm 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