Triangles
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Description of triangles
- A triangles interior angles add up to 180 degrees.
- They have three sides.
- Triangles are sometimes similar; when they have the same scale factor.
Similar triangles
Triangles are similar when they have 2 congruent angles, when the 3 sides are proportional, when you're given two proportional sides and a congruent included angle.
Congruent Triangles
Triangle Congruence
Side Side Triangle:
If two triangles have the same side lengths, then the triangles are congruent. Another way to think of this theorem is that given three sides, there is only one triangle with these measurements.
Side-Anlge-Side:
If two triangles have two sides and the included angles equal, respectively, then the triangles are congruent. Another way to think of this theorem is that given two sides and an included angle, there is only one triangle with these measurements.
Pythagorean Theorem
The Pythagorean theorem deals with the lengths of the sides of a right triangle. It is often written in the form of the equation:
a2 + b2 = c2
The theorem states that:
The sum of the squares of the lengths of the legs of a right triangle ('a' and 'b' in the triangle shown below) is equal to the square of the length of the hypotenuse ('c').
Example: You are given a right triangle with the side length of {side a}=5 and {side b}=7. To find the length for side c, you would just plug those numbers into the pythagorean eqaution.
5^2+7^2=c^2
25+49=c^2 ...... 74=c^2
to find C all you would do is undue the squared side so you would have to square root both sides because that is the oppisite of squaring.
answer: c=37
