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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Identify each quadrilateral. 1. quadrilateral with 4 right angles 2. quadrilateral with 2 pairs of parallel sides 3. quadrilateral with 4 congruent sides and t no right angles. rectangle. parallelogram. rhombus.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Identify each quadrilateral. 1. quadrilateral with 4 right angles 2. quadrilateral with 2 pairs of parallel sides 3. quadrilateral with 4 congruent sides and t no right angles rectangle parallelogram rhombus

  3. California Standards Extension of MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

  4. Vocabulary tessellation regular tessellation

  5. A repeating pattern of plane figures that completely covers a plane with no gaps or overlaps is a tessellation.

  6. In a regular tessellation, a regular polygon is repeated to fill a plane. The angles at each vertex add to 360°,so exactly three regular tessellations exist.

  7. Additional Example 1: Creating a Tessellation Create a tessellation with quadrilateral EFGH. There must be a copy of each angle of quadrilateral EFGH at every vertex.

  8. J K L I Check It Out! Example 1 Create a tessellation with quadrilateral IJKL. There must be a copy of each angle of quadrilateral IJKL at every vertex.

  9. Additional Example 2: Creating a Tessellation by Transforming a Polygon Use rotations to create a tessellation with the quadrilateral given below. Step 1: Find the midpoint of a side. Step 2: Make a new edge for half of the side. Step 3: Rotate the new edge around the midpoint to form the edge of the other half of the side. Step 4: Repeat with the other sides.

  10. Additional Example 2 Continued Step 5: Use the figure to make a tessellation.

  11. Check It Out! Example 2 Use rotations to create a tessellation with the quadrilateral given below. Step 1: Find the midpoint of a side. Step 2: Make a new edge for half of the side. Step 3: Rotate the new edge around the midpoint to form the edge of the other half of the side. Step 4: Repeat with the other sides.

  12. Check It Out! Example 2 Continued Step 5: Use the figure to make a tessellation.

  13. Lesson Quiz 1. Explain why a regular tessellation with regular octagons is impossible. Each angle measure in a regular octagon is 135° and 135 is not a factor of 360. 2. Can a semiregular tessellation be formed using a regular 12-sided polygon and a regular hexagon? Explain. No; a regular 12-sided polygon has angles that measure 150° and a regular hexagon has angles that measure 120°. No combinations of 120° and 150° add to 360°

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