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EOCT Review

Unit 5 – Transformations in the Plane Unit 6 – Connecting Algebra with Geometry. EOCT Review. Key Ideas. Precise definitions: Angle Circle Perpendicular lines Parallel lines Line Segment. Unit 5 - Transformations. Represent transformations in the plane Compare rigid and non-rigid

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EOCT Review

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  1. Unit 5 – Transformations in the Plane Unit 6 – Connecting Algebra with Geometry EOCT Review

  2. Key Ideas • Precise definitions: • Angle • Circle • Perpendicular lines • Parallel lines • Line Segment

  3. Unit 5 - Transformations • Represent transformations in the plane • Compare rigid and non-rigid • Translations • Rotations • Reflections • Understand Dilations

  4. Key Ideas • Given shapes – • Determine which sequence of rotations and reflections would map it on itself • Develop definitions of rotations, reflections and translations

  5. Translations A translation maps every two points P and Q to points P' and Q' so that the following properties are true: ● PP' = QQ' ● PP' QQ'

  6. Reflections A reflection across a line m maps every point R to R' so that the following properties are true: ● If R is not on m, then m is the perpendicular bisector of RR' . ● If R is on m, then R and R' are the same point.

  7. Rotations A rotation of x° about a point Q maps every point S to S' so that the following properties are true: ● SQ = S' Q and m<SQS' = x° . ● Preimage point Q and image point Q' are the same. Note: QS and QS' are radii of a circle with center Q.

  8. Examples Use the translation (x, y) → (x – 3, y + 1).

  9. Examples Describe every transformation that maps the given figure to itself.

  10. Unit 6 – Connecting Algebra and Geometry • Use coordinates to prove simple geometric theorems algebraically. • Circle centers • Parallelograms • Rectangles • Squares and Rhombii

  11. Geometric Problems • Prove lines parallel or perpendicular • The slope of the line through points (x1, y1) and (x2 , y2 ) is • Find the equation of a line through a given point • y=mx+b

  12. Distance Formula

  13. Exterior Angle Theorem m<1= m<2+m<3

  14. Key Ideas • Partition a directed segment into a given ratio.

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