Unit 1: Introduction to Geometry
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Unit 1: Introduction To Geometry
1.1 Geometry Vocabulary
1.2 Segment Addition Postulate, and Bisector
1.3 Distance & Midpoint
1.4 Angle Measure
1.5 Angle Relationships 1.1 Geometry Vocabulary
(Leave room on the right for pictures.)
The “Undefined” Terms
1. Point
2. Line
3. Plane
Definitions
4. Collinear points
5. Coplanar points
6. Coplanar lines
7. Noncollinear points
8. Noncoplanar points 9. Noncoplanar lines
10. Segment (line segment)
11. Parallel lines
12. Parallel planes
13. Skew lines
14. Congruent
15. Congruent segments
16. Midpoint
17. Segment bisector
18. Ray
19. Angle
20. Congruent angles
21. Right angle 22. Perpendicular lines
23. Acute angle
24. Obtuse angle
25. Straight angle
26. Angle bisector
27. Vertical angles
28. Complementary angles
29. Supplementary angles
30. Linear pair (Linear pair angles) 1.2 Segment Addition Postulate
Ex. 1. S, D, and T are collinear, and S is between D and T. If DT = 40, DS = 2x -8, and ST = 3x – 12, find x, DS, and ST.
Ex. 2. S, R, and T are collinear, and S is between R and T. If RS = 3x + 4, ST = 2x – 5, and RT = 34, find x and ST. 1.2/1.3 Midpoints, Bisectors, and Vertical Angles
Notation -
Segments Angles
Midpoints
Ex. 1 If C is the midpoint of AB, AC = 3x + 1, CB = 2x + 4, find x, AC, CB, and AB.
Ex. 2 If D is the midpoint of EF, ED = 3x + 1, EF = 4x + 12, find x, ED, DF, and EF. Segment Bisectors
Ex. 3 DB bisects AC at E, AE = 2x + 6 and AC = 36, find x, AE, and EC.
Angle Bisectors
Ex. 4 If BX bisects ABC, mABX = 6x, and mXBC = 3x + 21, find x, mABX, and mABC.
Vertical Angles
Ex. 5 1 and 2 are vertical angles. If m1 = x + 3 and m2 = 5x – 25, find x and m1. 1.4 Angle Addition Postulate
Ex. 1) Point D is in the interior of ∠ABC. m∠ABC = 4x - 20, mABD = x - 4, mDBC = x + 6. Find x and mABC.
Ex 2) Point D is in the interior of ∠ABC. mABC = 108˚, mABD = x, and mDBC is 2 times
bigger than mABD. Find x and mDBC. 1.5 Complementary and Supplementary Angles
Complementary Angles -
Ex. 1 In the picture above, m1 = x + 8 and m2 = x + 2. Find x and m2.
Ex. 2 5 is the complement of 6. If m5 = 2x – 4 and m6 = x + 16, find x and m6.
Supplementary Angles - Linear Pair –
Ex. 3 In the picture above, m1 = 6x + 20 and m2 = 2x. Find x and m1.
Ex. 4 3 and 4 are a linear pair. m3 = 2x – 5 and m4 = 3x + 45. Find x and m4.
Ex 5 In the picture to the right, find x and mABE.