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"Tri" These IVIissing Angles
"Tri" These IVIissing Angles

... Interior and Exterior Angles In the diagram below, angles a, b, and c are interior angles. Angle x is an exterior angle. The sum of the measures of the interior angles a and b is equal to the measure of the exterior angle x. ...
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... horizontal line and a line of sight to a point above the line. • An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. • Angles of elevation and depression are congruent because they are alternate interior angles. ...
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... Linear Pair of Angles ...
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... 6. Identify all pairs of congruent corresponding parts of congruent figures. 7. Determine if figures are congruent. 8. Appreciate that congruent triangles can be used to find distances that are difficult to measure directly. 9. Determine measurements of all three angles of an isosceles triangle when ...
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Section 5.5 ~ Inequalities in a Triangle

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Geometry Study Guide for Chapter 1

CHAPTER 7 Similarity Theorems  1.  Angle-Angle Similarity (AA~) Postulate:
CHAPTER 7 Similarity Theorems 1. Angle-Angle Similarity (AA~) Postulate:

... If the corresponding sides of two triangles are proportional, then the triangles are similar. 4. Right Triangle Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. 5. Heartbeat Corollary ...
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Comparing Planar and Spherical Geometry

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... triangle are congruent to two sides of another triangle, but the 3rd side of the first triangle is longer than the 3rd side of the second, then the included angle of the first triangle is larger than the included angle of the second. Fancy talk for two sides same, one sidee bigger than other, then a ...
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Geometric Shapes with Given Conditions Matching Worksheet

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... Section 5.4 Theorem 5.11 Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A All of the following must be true: AB+BC>AC BC+AC>AB B AC+AB>BC C *Theorem 5.11 is used to determine whether the three given segments can form ...
Point of Contact Triangle - Mathematical Association of America
Point of Contact Triangle - Mathematical Association of America

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Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions like sine and cosine by substituting their squared equivalents. Wildberger draws inspiration from mathematicians predating Georg Cantor's infinite set-theory, like Gauss and Euclid, who he claims were far more wary of using infinite sets than modern mathematicians. To date, rational trigonometry is largely unmentioned in mainstream mathematical literature.
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