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G T5 Resources Similarity Study Material.pptx

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LuisSalenga1

This document discusses key concepts related to similarity in geometry, including definitions of similar figures, scale factors, and different methods of proving similarity between triangles. It introduces several similarity transformations, such as dilations, translations, and rotations. Examples are provided to illustrate proportional side lengths and equal angles as properties of similar figures.

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Geometry Topic 5 Similarity
Vocabulary
Choose 3-4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Mathematically Speaking! Examples of accuracy line vs line segment translation vs slide midpoint vs the middle
Betweenness given three points A, B, and C, B is between A and C if and only if all three of the points lie on the same line, and AB + BC = AC. A C B
Congruent having the same size and shape, denoted by . 基巨 倹乞 基 駒
Scale factor in a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the preimage. Scale Factor = 9 3 = 3
Similar Figures figures with the same shape (but not necessarily the same size) and the following properties: Corresponding sides are proportional. That is, the ratios of the corresponding sides are equal. Corresponding angles are equal.
Similarity transformation a transformation that results in an image that is the same shape, but not necessarily the same size, as the original figure.
Dilation a transformation in which the lines connecting every point with its preimage all intersect at a point known as the center of dilation, and 咋 咋 is the same for every point ; a transformation that changes the size of a figure but not its shape. G
Side-Side-Side similarity if the corresponding side lengths of two triangles are proportional, then the triangles are similar.
Side-Angle-Side similarity if the lengths of two pairs of corresponding sides of two triangles are proportional and the angles the sides form are congruent, then the triangles are similar.
Angle-Angle similarity If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
Side Splitter Theorem If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally. = = 瑞

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G T5 Resources Similarity Study Material.pptx

  • 3. Choose 3-4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Mathematically Speaking! Examples of accuracy line vs line segment translation vs slide midpoint vs the middle
  • 4. Betweenness given three points A, B, and C, B is between A and C if and only if all three of the points lie on the same line, and AB + BC = AC. A C B
  • 5. Congruent having the same size and shape, denoted by . 基巨 倹乞 基 駒
  • 6. Scale factor in a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the preimage. Scale Factor = 9 3 = 3
  • 7. Similar Figures figures with the same shape (but not necessarily the same size) and the following properties: Corresponding sides are proportional. That is, the ratios of the corresponding sides are equal. Corresponding angles are equal.
  • 8. Similarity transformation a transformation that results in an image that is the same shape, but not necessarily the same size, as the original figure.
  • 9. Dilation a transformation in which the lines connecting every point with its preimage all intersect at a point known as the center of dilation, and 咋 咋 is the same for every point ; a transformation that changes the size of a figure but not its shape. G
  • 10. Side-Side-Side similarity if the corresponding side lengths of two triangles are proportional, then the triangles are similar.
  • 11. Side-Angle-Side similarity if the lengths of two pairs of corresponding sides of two triangles are proportional and the angles the sides form are congruent, then the triangles are similar.
  • 12. Angle-Angle similarity If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
  • 13. Side Splitter Theorem If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally. = = 瑞