GSE Geometry Semester 1

01 Points, Lines and Planes

04 Angles

62 Translations

63 Rotations

Rotation of -90° clockwise about the origin (x, y) → (y, -x)Rotation of -180° clockwise about the origin (x, y) → (-x, -y)Rotation of -270° clockwise about the origin (x, y) → (-y, x)

Rotation

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64 Reflections

For a reflection across the line y = -x,

Size and Reflections

Transformation – Nothing new in this less not covered in other lessons.32 Congruence Transformations

65 Compositions of Transformations

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66 Dilations

Dilations - The scale factor k of a dilation is the ratio of the length in the image to the corresponding length in the

preimage (original image). (k = image length

pre−image length )

http://www.mathbitsnotebook.com/Geometry/Similarity/SMdilation.htmlk > 1 Enlargement 0 < k < 1 Reduction

k = 1 Same as the preimagek < 0 180 ° rotation and dilation by scale factor |k|

45 Similarity Transformations

39 Similar Polygons

∆ ABC ∆ XYZMeans that ¿ A <X¿ B <Y¿C <Z

75 Changing Dimensions

40 Proving Triangles Similar – AA, SSS and SASReflexive Property of Angle CongruenceAny angle is congruent to itself.

Substitution Property of EqualityDivision Property of EqualitySegment Addition Postulate

Corresponding Angles Postulate

05 Basic ConstructionsCongruent SegmentsCongruent AnglesAngle Bisectors

15 Geometric Proof – Part 1

16 Geometric Proof – Part 2

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Unit 4 – 17 – Lines and Transversals

18 Angle Pair Theorems

20 Perpendicular Lines

21 More Geometric Constructions

26 Angles of Triangles

27 Congruence

28 Congruence Theorems and Postulates, SSS and SAS

29 Congruence Theorems and Postulates, ASA and AAS

30 Congruence Theorems and Postulates, HL

32 Congruence Transformations

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Unit 5 - 33 Segments and Angles in Triangles

35 Constructing Special Points in Triangles

41 Right Triangle Similarity

42 Segments in Similar Triangles

44 Proportional Relationships

56 Parallelograms

57 Conditins for Parallelograms

60 Coordinate Geometry

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Unit 6 – 46 The Pythogorean Theorem

47 The Converse of the Pythogorean Theorem

48 Special Right Triangles

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Unit 7 – 49 The Tangent Ratio

50 The Sine and Cosine Ratios

sine = oppositehypotenuse cosine =

adjacenthypotenuse

51 Solving Right Triangles

52 Right Triangle Applications

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