Geometry similar triangles
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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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Geometry: Similar Triangles

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Geometry similar triangles

Geometry: Similar Triangles


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 and similar triangles1

Congruent and similar triangles

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


Congruent and similar triangles and geometric transformations

Congruent and similar triangles and geometric transformations


Geometric transformations of triangle

Geometric transformations of triangle:


Examples of transformations reflection

Examples of transformations: reflection


Examples of transformations dilation

Examples of transformations: dilation


Examples of transformations translation by a vector

Examples of transformations: translation by a vector


Examples of transformations rotation

Examples of transformations: rotation


Examples of transformations reflection at a point

Examples of transformations: reflection at a point


Answers to exercises

Answers to exercises:

  • Rotation ex1.ggb

  • Reflection about a line ex2.ggb

  • Translation by vector ex3.ggb

  • Scaling ex4.ggb


Congruent and similar triangles and coordinate geometry

Congruent and similar triangles and coordinate geometry


Congruent triangles

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.


Congruent triangles1

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.


Congruent triangles2

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


Similar triangles

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.


Similar triangles1

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


Guided exercise

Guided exercise

Use graphic paper for Question 1 in handout


Final remarks and discussion

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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