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In a 30°-60°-90° triangle,  the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg

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In a 45°-45°-90° triangle, the hypotenuse is √2 times as long as the leg

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The square of the longest side of the triangle is greater than the sum of the squares of the other two sides, then the triangle is an obtuse triangle -

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If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is an acute triangle ->

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If the square of one side of a triangle is equal to the sum of the square on the other two sides, then the triangle is a right triangle ->

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In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs

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If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

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Corollary 1: When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.

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Corollary 2: When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg

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SAS (Side-Angle-Side) Similarity Theorem 8.3.3 

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SAS (Side-Angle-Side) Similarity Theorem 8.3.3 

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If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar

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SSS (Side-Side-Side) Similarity Theorem 8.3.2

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SSS (Side-Side-Side) Similarity Theorem 8.3.2

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If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

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For any triangle △ABC with sides a,b, and c:

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For any triangle △ABC with sides a, b, and c:

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AA (Angle-Angle) Triangle Similarity Postulate 8.3.1

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AA (Angle-Angle) Triangle Similarity Postulate 8.3.1

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If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

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a triangle with no right angle; it either has all 3 acute angles or 1 obtuse angle and 2 acute angles,

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the way towards which an object moves or tends; where something is pointing

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size of a mathematical object; property that determines whether the object is larger or smaller than other objects of the same kind

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an object that has both magnitude and a direction; captured as a line segment where length = magnitude and arrow = direction

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used to understand sines and cosines of angles found in right triangles. It has a center at the origin (0,0) and a radius of 1 unit. radius starts in quadrant 1/positive x axis and continues around the unit circle

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a trigonometric function whose value for the complement of an angle is equal to the value of a given trigonometric function of the angle itself

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triangles with equal corresponding angles and proportionate sides

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A right triangle with angles 30-60-90; their ratio is
x : x√3 :2x

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A type of isosceles right triangle where the two legs are congruent to one another and are non right angles equal to 45 degrees ; many times we use the pythagorean theorem to solve;
x : x : x√2

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used for calculating one side of a triangle when the angle opposite and the other two sides are known; SSS & SAS

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used to find angles of a general triangle; ASA & AAS

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ratios that help to find the angle using the sides rather than using one angle and one side to find another side; can also be called arc

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the longest side of the triangle; opposite of the right angle

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the side across from said angle

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I found these helpful and essential this quarter !!

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S OH C AH T OA

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"lie near"; the side that lies next to the said angle

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the opposite side of a triangle to the adjacent which gives the value of tan

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Terms & Definitions
* yellow sticky notes *

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the branch of mathematics that deals with triangles; particularly right triangles & the ratios and their relationships with the sides and angles

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the opposite side of a right triangle to the hypotenuse which gives the value of sine

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the adjacent side of a triangle to the hypotenuse gives the value of cosine