Download Congruent and Similar Triangles (MASMTS408).notebook

Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
Congruent Triangles
Two triangles are congruent when all three corresponding sides and all three corresponding angles have the same measurements.
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To prove that two triangles are congruent, it is not necessary to show all six conditions. (Note: Isometric and congruent mean the same thing.)
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
There are minimum conditions for showing that triangles are congruent. These are known as Theorems of Congruence.
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1) If the three sides of one triangle are congruent to the three corresponding sides of another triangle, then the triangles are congruent. This is called the Side Side Side theorem (SSS).
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
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2) If two sides and the contained angle of one triangle are congruent to two corresponding sides and contained angle of another triangle, then the triangles are congruent. This is called the Side Angle Side theorem (SAS).
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
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3) If two angles and the contained side of one triangle are congruent to two corresponding angles and contained side of another triangle, then the triangles are congruent. This is called the Angle Side Angle theorem (ASA).
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
Similar Triangles
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Two figures are similar when ...
All corresponding angles are congruent.
All corresponding sides are proportional.
Therefore, similar figures have the same shape, but are not necessarily the same size.
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
There are also minimum conditions to prove that two triangles are similar.
1) Side Side Side (SSS)
If the corresponding sides of two triangles are proportional in length, then the triangles are similar.
2) Angle Angle (AA)
If two corresponding angles of two triangles are congruent, then the triangles are similar.
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3) Side Angle Side (SAS) If two triangles have one congruent angle contained between corresponding sides of proportional length, then the triangles are similar.
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
Name the similar triangles and why they are similar.
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
Similar Triangles
Knowing that triangles are similar allows us to solve some geometric problems.
Example: Given that the triangles below are similar, solve triangle DEF. (To solve a triangle is to find all its measures.)
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Set up a proportion: 8
Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
Example: Determine the value of x.
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Congruent and Similar Triangles (MASMTS408).notebook
February 27, 2014
Example:Determine the value of x.
Triangles are similar by AA
Separate the triangles
and make their
orientations the same.
Set up and solve the proportion
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