Name an angle by its vertex and use angle addition to find missing measures, including a worked algebra example.
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Use the perpendicular radius and the Pythagorean theorem to check tangency or find a missing radius. Includes the two tangents theorem.
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Read the net of a right circular cone, distinguish height from slant height, and use both formulas in worked examples.
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Use two angles and a nonincluded side for AAS, or a hypotenuse and leg for HL. See why general SSA can give two triangles.
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Match the vertices of congruent triangles and use CPCTC to prove that corresponding sides or angles are congruent. Includes a shared-side proof.
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A 45-45-90 triangle is a special kind of right triangle, because it’s isosceles with two congruent sides and two congruent angles. Since it’s a right triangle, the length of the hypotenuse has to be greater than the length of each leg, so the congruent sides are the legs of the triangle.
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A 30-60-90 is a scalene triangle and each side has a different measure. Since it’s a right triangle, the sides touching the right angle are called the legs of the triangle, it has a long leg and a short leg, and the hypotenuse is the side across from the right angle. In this lesson we’ll look at how to solve for the side lengths of a 30-60-90 triangle.
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Write an if-then statement, identify its hypothesis and conclusion, and draw Euler diagrams for nested and disjoint sets.
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Swap the hypothesis and conclusion to write the converse. Use an Euler diagram and a counterexample to check whether it’s true.
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Use clockwise and counterclockwise rules for 90°, 180°, and 270°, then rotate a point around a center other than the origin.
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Tell SSS, ASA, and SAS apart, find the included side or angle, and match corresponding vertices in a congruence statement.
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Use the 360-degree exterior angle sum, find the exterior angle of a regular polygon, and solve three worked examples.
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Find slopes from two points and compare them. Covers negative reciprocals, coincident lines, and horizontal and vertical cases.
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Find an inscribed angle from its intercepted arc or central angle. Includes a major arc example that uses the full 360 degrees.
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Compare the properties of quadrilaterals, then use consecutive angles and equal diagonals to solve two geometry examples.
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Use the Pythagorean theorem to find the distance between two points in space. Work through an integer answer and an exact radical.
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Find the common vertex and ray, check whether the interiors overlap, and name adjacent pairs in a diagram.
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Write the standard equation of a circle, read its center and radius, find intercepts, and convert general form by completing the square.
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Put if–then statements in order, fill in a missing conditional, and use the law of syllogism to write the conclusion.
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Multiply the base by the perpendicular height. Work through labeled dimensions, a grid, and a height found with the Pythagorean theorem.
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