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Cube Roots

"A square root is an exponent of one-half. A cube root is an exponent of one-third. Square roots of negative numbers do not have real number roots since the product of any real number and itself is po ...

Quadratic Equation Applications

"In Algebra I and Algebra II, we sometimes need to solve word problems using quadratic equations. When solving word problems, some common quadratic equation applications include projectial motion prob ...

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 ...

Pythagorean Theorem Converse

"If we know that the sum of two square sides in a triangle equals the square of the third side, we can conclude that the triangle is a right triangle. Pythagorean triples are commonly seen side length ...

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 ...

Proportions

"We can find unknown quantities when we know similar ratios for comparison, using proportions. We find proportions often in word problems, for example those involving baking ingredients, and in compar ...

Cosine Ratios

"Right triangles have ratios that are used to represent their base angles. Cosine ratios, along with sine and tangent ratios, are ratios of two different sides of a right triangle. Cosine ratios are s ...

Proportional Segments

"When a line is drawn parallel to one side in a triangle, two similar triangles are formed because corresponding angles yield the AA similarity shortcut. Because the triangles are similar, the segment ...

Corresponding Parts of Triangles

"If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles. To find a missing angle bisector, altitu ...

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