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Properties and Theorems

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

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Properties and Theorems

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  1. Properties and Theorems

  2. 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 Alternate Interior Angles Theorem & Converse Consecutive Interior Angles Theorem & Converse Alternate Exterior Angles Theorem & Converse • 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

  3. List of Theorems Chapter 4 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 • 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

  4. 4.1 – Triangles and Angles

  5. Types of Triangles

  6. Types of Triangles

  7. Right and Isosceles Triangles

  8. Interior vs. Exterior Angles

  9. Triangle Sum Theorem

  10. Exterior Angle Theorem

  11. Corollary to the Triangle Sum Theorem

  12. Classify the triangle by its angles and by its sides.

  13. Classify the triangle by its angles and by its sides.

  14. Classify the triangle by its angles and by its sides.

  15. Complete the sentence with always, sometimes, or never.

  16. 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

  17. Find the measure of the numbered angles.

  18. Find the measure of the numbered angles.

  19. Find the measure of the exterior angle shown

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

  21. Find the measure of the exterior angle shown

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

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