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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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Block 29

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 congruent, regular and similar polygons, and to perform transformations in the plane


Congruent and similar triangles1
Congruent and similar triangles congruent, regular and similar polygons, and to perform transformations in the plane

  • Review of definitions, properties and theorems of congruent and similar triangles









Answers to exercises
Answers to exercises: transformations

  • Rotation ex1.ggb

  • Reflection about a line ex2.ggb

  • Translation by vector ex3.ggb

  • Scaling ex4.ggb



Congruent triangles
Congruent triangles transformations

  • 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.


Congruent triangles1
Congruent triangles transformations

  • 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.


Congruent triangles2
Congruent triangles transformations

  • 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


Similar triangles
Similar triangles transformations

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.


Similar triangles1
Similar triangles transformations

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


Guided exercise

Guided exercise transformations

Use graphic paper for Question 1 in handout


Final remarks and discussion
Final remarks and discussion transformations

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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