Properties and Theorems

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Presentation transcript:

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 Chapter 5 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 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. A right isosceles triangle An obtuse scalene triangle An acute equilateral triangle 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

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

Find the measure of the exterior angle shown

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