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Unit 05 (Jurgensen Theorems (5-13 Quadrilaterals: The diagonals of a…
Unit 05
Jurgensen Theorems
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5-15 Quadrilaterals: The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
5-11 Quadrilaterals: The segment that joins the midpoints of two sides of a triangle
(1) is parallel to the third side.
(2) is half as long as the third side.
5-16 Quadrilaterals: If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
5-10 Quadrilaterals: A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
5-17 Quadrilaterals: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.
5-9 Quadrilaterals: If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
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5-8 Quadrilaterals: If two lines are parallel, then all points on one line are equidistant from the other line.
5-19 Quadrilaterals: The median of a trapezoid
(1) is parallel to the bases.
(2) has a length equal to the average of the base lengths.
5-7 Quadrilaterals: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
13-1 The Distance Formula: The distance d between points (x1, y1) and (x2, y2) is given by: 
5-6 Quadrilaterals:If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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5-5 Quadrilaterals: If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
13-4 Coordinate Geometry: Two nonvertical lines are perpendicular if and only if the product of their slopes is -1.
5-4 Quadrilaterals: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
13-5 The Midpoint Formula: The midpoint of the segment that joins points (x1, y1) and (x2, y2) is the point
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13-6 Standard Form: The graph of any equation that can be written in the form Ax + By = C, with A and B not both zero, is a line.
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13-8 Point-Slope Form: An equation of the line that passes through the point (x1, y1) and has slope m is:
Holt Theorems
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Thm 4.5.13: The diagonals of a square are congruent and are the perpendicular bisectors of each other.
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Thm 4.6.1: If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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Thm 4.6.2: If one pair of opposite sides of a quadrilateral are parallel and congruent then the quadrilateral is a parallelogram.
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Thm 4.6.3: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
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Thm 4.6.4: If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
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4.6.5 Housebuilder Theorem: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
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Thm 4.6.6: If one pair of adjacent sides of a parallelogram are congruent, then the quadrilateral is a rhombus.
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Thm 4.6.7: If the diagonals of a parallelogram bisect the angles of the parallelogram, then the parallelogram is a rhombus.
3.6.3 Sum of Exterior Angles of a Polygon: The sum of the measures of the exterior angles of a polygon is 360 degrees.
Thm 4.6.8: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
3.6.2 Measure of Interior Angles of a Polygon: The measure, m, of an interior angle of a regular polygon with n sides is given by m=180 degrees-(360 degrees/n).
4.6.9 Triangle Midsegment Theorem: A midsegment of a triangle is parallel to a side of the triangle, and its length is equal to half the length of that side.
3.6.1 Sum of Interior Angle of a Polygon: The sum, s, of the measures of the interior angles of a polygon with n sides is given by s=(n-2)(180 degrees).
Vocabulary
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midsegment of triangle: an angle formed between one side of polygon and the extension of an adjacent side
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midsegment of trapezoid: a line connecting the midpoints of the two nonparallel segments of a trapezoid
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