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Finding the similarities of triangles. A triangle can be similar to another triangle by having the same angles but the triangles are not the same size or having all sides of both triangles divisible by a common denominator.

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Determine whether a parallelogram is a rectangle or rhombus.

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When two or more parallel lines intersect other lines, proportional segments are formed.
For example: If... then...

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6.2

M1+m2+M3+M4+M5=360

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Veronica 7.4 Similarity in Right Triangles

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Veronica 7.4 Similarity in Right Triangles

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When you draw the altitude to the hypotenuse of a right triangle, you form three pairs of similar right triangles.
Theorem 7:3- the altitude of the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
Corollary 1: the length of the altitude to the hypotenuse of the right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
Corollary 2: the altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to the leg.

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Similar figures have the same shape but not necessarily the same size. You can abbreviate is similar to with the symbol

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Polygon Angle Sum Theorem: The sum of the measures of the interior angles of an n-gon is (n-2) 180

The measure of each interior angle of a regular n-gon is (n-2) 180/n

The sum of the interior angle measures of a polygon depends on the number of sides the polygon has.

By dividing a polygon with n sides into (n-2) triangles, you can show that the sum of the interior angle measures of any polygon is a multiple of  180.

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An angle of elevation (depression) is the angle formed by a horizontal line and the line of sight to an object above (below) the horizontal line
The angle of depression is congruent to the angle of elevation because they are alternate interior angles
Place your finger on the vertex of the angle. Trace along the non horizontal side of the angle. See if you finger is above (elevation) or below (depression) the vertex

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Sin (A)= opposite : hypotenuse
Cos (A) = adjacent : hypotenuse
Tan (A) = opposite : hypotenuse

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John 6.3 Proving A quadrilateral is a parallelogram

► If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
► If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
► If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

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In 6.6 there are four theorems about the properties of trapezoids.

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Right triangles have properties that allow you to use shortcuts to determine side lengths without using the Pythagorean theorem.

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Elian 8.6 The law of sines relates the sine of each angle to the length of the opposite side.

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Elian 8.6 The law of sines relates the sine of each angle to the length of the opposite side.