Proportion and Reasoning
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Transcript Proportion and Reasoning
Take out your calculator
What does it mean for two triangles
to be similar?
What information is sufficient to
show that two triangles are similar?
Draw and label an example of two
similar triangles.
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Common Mistakes
Establish expectations
Define the sine, cosine, and tangent ratios
Understand the usefulness of trigonometry
Use problem solving skills
Trigonometry is the study of the relationships
between the sides and the angles of a triangle.
In this lesson you will discover some of these
relationships for right triangles.
All these triangles are similar by SAS
or AA.
Notice that the ratio of the shorter
leg’s length to the longer leg’s
length is 3/5. The angle opposite
the shorter leg is 31o.
The three right triangles are similar
to each other by AA
Sine (sin) is the ratio of the length of the
opposite leg to the length of the hypotenuse.
◦ Sin (A) =opposite/hypotenuse
◦ S=O/H
Cosine (cos) is the ratio of the length of the
adjacent leg to the length of the hypotenuse.
◦ Cos (A)=adjacent/hypotenuse
◦ C=A/H
Tangent (tan) is the ratio of the length of the
opposite leg to the length of the adjacent leg.
◦ Tan (A)=opposite/adjacent
◦ T=O/A
SOH-CAH-TOA
Some Old Horse Caught Another Horse
Taking Old Apples
Memorize all the trig ratios (including
working backwards)
Establish expectations
Define the sine, cosine, and tangent ratios
Understand the usefulness of trigonometry
Use problem solving skills