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Remote Interior Angles

"If one side of a triangle is extended beyond the vertex, an exterior angle is formed. This exterior angle is supplementary with its adjacent, linear angle. Since the angle sum in a triangle is also 1 ...

Regions Between Circles and Squares

"A common application of the area of a circle and the area of a square are problems where a circle is circumscribed about a square or inscribed in a square. Regions between circles and squares problem ...

Reflectional Symmetry

"Symmetry in a figure exists if there is a reflection, rotation, or translation that can be performed and the image is identical. Reflectional symmetry exists when the figure can be folded over onto i ...

Distance Formula

"Using what we know about the Pythagorean theorem, we are able to derive the distance formula which is used to find the straight distance between two points in a coordinate plane. The distance formu ...

Dilations

"A dilation is a non-rigid transformation, which means that the original and the image are not congruent. They are, however, similar figures. To perform dilations, a scale factor and a center of dilat ...

Radii to Tangents

"When a radius is drawn to a point of tangency, the angle formed is always a right (90 degree) angle. This fact is commonly applied in problems with two tangent segments drawn to a circle from a point ...

Deductive Reasoning

"Deductive reasoning is the process of reasoning logically from given statements to make a conclusion. Deductive reasoning is the type of reasoning used when making a Geometric proof, when attorneys ...

Pythagorean Theorem Proofs

"The Pythagorean theorem states that in a right triangle the sum of its squared legs equals the square of its hypotenuse. The Pythagorean theorem is one of the most well-known theorems in mathematics ...

CPCTC

"CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are ...

Counterexample

"Throughout Geometry, students write definitions and test conjectures using counterexamples. When writing definitions, counterexamples are useful because they ensure a complete and unique description ...

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