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Geometry: Similar Triangles

Geometry: Similar Triangles . MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane. Block 29. Congruent and similar triangles . Congruent and similar triangles .

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Geometry: Similar Triangles

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  1. Geometry: Similar Triangles

  2. MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane Block 29

  3. Congruent and similar triangles

  4. Congruent and similar triangles • Review of definitions, properties and theorems of congruent and similar triangles

  5. Congruent and similar triangles and geometric transformations

  6. Geometric transformations of triangle:

  7. Examples of transformations: reflection

  8. Examples of transformations: dilation

  9. Examples of transformations: translation by a vector

  10. Examples of transformations: rotation

  11. Examples of transformations: reflection at a point

  12. Answers to exercises: • Rotation ex1.ggb • Reflection about a line ex2.ggb • Translation by vector ex3.ggb • Scaling ex4.ggb

  13. Congruent and similar triangles and coordinate geometry

  14. Congruent triangles • SSS • If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. • ASA • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

  15. Congruent triangles • SAS • If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. • AAS • If two angles and a non included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the two triangles are congruent.

  16. Congruent triangles • Hyp-S • If the hypotenuse and the leg of one right triangle are congruent to the corresponding parts of the second right triangle, the two triangles are congruent

  17. Similar triangles Similar triangles have the same shape, but the size may be different. Two triangles are similar if: • two pairs of corresponding angles are congruent (therefore the third pair of corresponding angles are also congruent). OR • the three pairs of corresponding sides are proportional.

  18. Similar triangles • To find out if triangles given in coordinate geometry are similar you can check any of the properties using coordinate geometry like distance formula

  19. Guided exercise Use graphic paper for Question 1 in handout

  20. Final remarks and discussion Discuss in groups how you can teach topics in this section using web-based educational resources designed to reinforce learning ? Identify effective strategies for teaching Share your ideas in class discussion Answer the Question 2

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