Download Geometry: Similar Triangles - Math GR. 9-12

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
• 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:
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•
•
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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