Download Qtr 1 Theorem Notebook

H Geom Qtr 1
Name:
Block:
Seat:
Your Personally Illustrated Examples
of Definitions, Postulates, and Theorems
of Quarter 1
This first quarter we have begun our journey of making mathematical proofs. This quarter’s important
Definitions, Postulates and Theorems often used in proofs are listed in the next few pages of this pdf
document. For each:
1. Write out the definition, postulate, or theorem (try to make it a If-then statement).
2. Draw an example diagram to illustrate the hypothesis of the definition, postulate, or theorem.
3. State your example’s conclusion based on the definition, postulate, or theorem you are illustrating.
Example:
First we find the Ruler Postulate on page 9:
1. Write it as a conditional (“if-then”) statement (when possible):
“If you place a number line between two points, the distance between the points is the (absolute value
of the) difference between their coordinates”
2. Draw the hypothesis (feel free to draw your own here)
3. State the conclusion
XY = |5 − 2| = 3.
St. Francis High School
H. Geometry
Page 2 of 13
2016
Chapter 1
1. Ruler Postulate (p. 9)
2. Segment Addition Postulate (p. 10)
3. Protractor Postulate (p. 24)
4. Angle Addition Postulate (p. 25)
St. Francis High School
H. Geometry
Page 3 of 13
2016
Chapter 2
5. Perpendicular Lines (p. 73)
6. Point Line and Plane Postulates (p. 88)
St. Francis High School
H. Geometry
Page 4 of 13
2016
7. Properties of Equality (p. 97)
8. Distributive Property (p. 98),
St. Francis High School
H. Geometry
Page 5 of 13
2016
9. Reflexive, Symmetric and Transitive Properties of Equality (p. 99)
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H. Geometry
Page 6 of 13
2016
10. Linear Pair Postulate (p. 118)
11. Vertical Angles are Congruent (p. 118)
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H. Geometry
Page 7 of 13
2016
Chapter 3
12. Parallel Postulate (p. 140)
13. Perpendicular Postulate (p. 140)
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H. Geometry
Page 8 of 13
2016
14. Iff Corresponding Angles ∼
= the lines are || Postulate (p. 146,153)
15. Iff Alternate Interior Angles ∼
= the lines are ||Theorem (p. 147, 154)
St. Francis High School
H. Geometry
Page 9 of 13
2016
16. Iff Alternate Exterior Angles ∼
=the lines are || Theorem (p. 147, 154)
17. Iff Consecutive Interior Angles Supplementary, the lines are || Theorem (p. 147, 154)
18. Transitive Property of Parallel Lines (p. 156)
St. Francis High School
H. Geometry
Page 10 of 13
2016
Chapter 4
19. Triangle Sum Theorem (p. 208)
20. Exterior Angle Theorem (p. 209)
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H. Geometry
Page 11 of 13
2016
21. SSS (Side-Side-Side) (p. 232)
22. SAS (Side-Angle-Side) (p. 238)
23. HL (Hypotenuse-Leg) (p. 239)
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H. Geometry
Page 12 of 13
2016
24. ASA (Angle-Side-Angle) (p. 247)
25. AAS (Angle-Angle-Side) (p. 247)
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H. Geometry
Page 13 of 13
2016
26. Corresponding Parts of ∼
=∆∼
= (CPCTE or CP ∼
=∆∼
=) (p. 256)
27. Base Angle and Converse of Base Angle Theorems (aka. Isosceles Triangle Theorem) (p. 264)
St. Francis High School
H. Geometry