Student Tutorial: Triangle Definitions

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Study these triangle definitions.

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Triangle. A three-sided figure with three interior angles and three vertices. The sum of the three interior angle measures is 180°.

Triangle. A three-sided polygon that has three angles, vertices, and sides. The sum of the interior angles of a triangle is equal to 180°.

Area of a Triangle. The formula for finding the area of a triangle is one half the product of the base and height.

Perimeter of a Triangle. The perimeter of a triangle is found by adding the three side lengths of the triangle.

Triangle Altitude. Also called the “height,” the segment perpendicular to the base and intersecting the opposite vertex.

Vertex of a Triangle. The point where two sides of a triangle intersect. The “corner” of a triangle. Every triangle has three

Base of a Triangle. One of the sides of a triangle whose length is used in calculating the area of the triangle.

Acute Triangle. A triangle whose three interior angles are not greater than 90° in measure.

Incenter of a Triangle. Where the angle bisectors of a triangle intersect. It also is the center of an inscribed circle

Obtuse Triangle. A triangle, one of whose interior angles is greater than 90° in measure.

Isosceles Triangle. A triangle with two congruent sides and congruent base angles.

Isosceles Triangle. A triangle with two congruent sides. The perpendicular bisector of the base is the angle bisector of angle ABC.

Equilateral Triangle. A triangle with three congruent sides and three congruent interior angles.

Interior Angles of a Triangle. The three angles at the vertices of a triangle. The sum of the interior angles of a triangle is 180°.

Right Triangle. A triangle with one right angle and two acute angles. The relationship among the sides is summarized by the Pythagorean Theorem.

Hypotenuse. In a right triangle, the side opposite the right angle.

Pythagorean Triples. Three positive integers, a, b, and c, that follow the Pythagorean Theorem. When used as side lengths for a triangle, they form a special right triangle.

3, 4, 5 Right Triangle. A special right triangle whose sides are in the ratio shown below. All triangles similar to this triangle maintain this ratio.

5, 12, 13 Right Triangle. A special right triangle whose sides are in the ratio shown below. All triangles similar to this triangle maintain this ratio.

45°, 45°, 90° Right Triangle. A right triangle whose interior angles are 45°, 45°, and 90°. The sides are in the ratio shown below, which makes it an isosceles right triangle.

30°, 60°, 90° Right Triangle. A right triangle whose interior angles are 30°, 60°, and 90°. The sides are in the ratio shown below.