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Panorama 4

Panorama 4. From Lines to Geometric Transformations. Unit 4.1: Angles, Geometric Transformations & Rotation . ANGLES Ray: is a straight line that begins at a point of origin and extends in a certain direction. Angles: are made up of two rays that share the same origin.

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Panorama 4

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  1. Panorama 4 From Lines to Geometric Transformations

  2. Unit 4.1: Angles, Geometric Transformations & Rotation ANGLES • Ray: is a straight line that begins at a point of origin and extends in a certain direction.

  3. Angles: are made up of two rays that share the same origin. • This point is called the vertex. • The two rays are called the sides of the angle. • An arc is used to show the opening of the angle Side Arc Vertex Side

  4. Angles are usually named by its vertex. • Three letters are usually used. • The middle letter is always the vertex. Ex: ABC A B C

  5. “∠” means angle • “m∠” means angle measure. • Ex: m∠B = 35⁰ or m∠ABC = 35⁰ • To measure an angle you must use your protractor.

  6. To use the protractor place the center point at the vertex and one side on the “0” line.

  7. Zero Angle: m∠ = 0⁰ Acute Angle: m∠ = less than 90⁰ Obtuse Angle: m∠ = more than 90⁰ Right Angle: m∠ = 90⁰

  8. Straight Angle: m∠ = 180⁰ Reflex Angle: m∠ = 180⁰ to 360⁰ Full Angle: m∠ = 360⁰

  9. Geometric Transformations • A geometric transformation is used to “pair up” a mirror image with an initial image • Mirror image is always read as “prime” A A1 C1 C B B1

  10. Rotation • Rotation is moving an initial image around a given point. • This point is called the center of rotation. • You can move clockwise or counter-clockwise. • Counter-clockwise is always positive • Clockwise is always negative.

  11. Steps to follow for performing rotations: • Draw a line from each point to the center of rotation. • Place the center of your protractor on the center of rotation and the 0 line on the line you have drawn. • Measure the angle specified and mark it • Draw another line from the mark you have made to the center of rotation.

  12. Measure the distance from your initial point to the center of rotation with your compass. • Use that measurement to make an arc on the second line you have drawn. • Where the arc and the line meet that is where your point should be. • Repeat steps 2-7 for each point. • Label each point as prime • Connect all of your new points.

  13. Angle Center of Rotation

  14. Classwork and Homework Textbook: p 168-171 # 1-13 Workbook: p 53-55

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