Geometry: Similar Triangles. MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations.

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Presentation transcript:

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

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

Congruent and similar triangles and geometric transformations

Geometric transformations of triangle:

Examples of transformations: reflection

Examples of transformations: dilation

Examples of transformations: translation by a vector

Examples of transformations: rotation

Examples of transformations: reflection at a point

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 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 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 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 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 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 Use graphic paper for Question 1 in handout

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