Transcript Similar Triangles

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Information
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Proving triangles similar
Triangles are similar when corresponding angles are
congruent and corresponding sides have the same ratio.
Prove that △ABC ~ △DEC.
show corresponding angles are congruent:
19.7
reflexive property
of congruence:
∠BAC ≅ ∠DAE
corresponding
angles postulate:
∠ADE ≅ ∠ABC 

∠AED ≅ ∠ACB 
26.3
35.3
16.9
15.6
28.0
show corresponding sides have the same ratio:

AE/AC = 28.0/(28.0+15.6) = 0.64 
AD/AB = 35.3/(35.3+19.7) = 0.64
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DE/BC = 16.9/26.3 = 0.64 
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Using similarity in triangles
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Exploring similarity postulates
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Establishing the AA similarity postulate
Angle-angle similarity postulate:
If two angles of a triangle are congruent to two angles of
another triangle, then the two triangles are similar.
● If two triangles are similar, they are
related by similarity transformations.
● Rotation, reflection and transformation
preserve angles and side lengths.
● Dilation preserves angle but changes
the sides lengths proportionally.
● If two angles of a triangle are specified,
the third one is also determined.
● Therefore, two triangles with two
congruent angles are similar.
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Similar triangles
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Summary activity
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