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What is the sum of the interior angles in any triangle?
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The sum of the interior angles in any triangle is 180 degrees.
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Define an equilateral triangle.
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An equilateral triangle is a triangle where all three sides are of equal length, and all three interior angles are 60 degrees each.
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What characterizes a right triangle?
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A right triangle has one angle that is exactly 90 degrees.
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How do you calculate the area of a triangle?
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The area of a triangle is calculated by the formula: 1/2 * base * height.
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What is the Pythagorean theorem used for?
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The Pythagorean theorem is used to calculate the length of a side in a right triangle: a² + b² = c², where c is the hypotenuse.
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Define an isosceles triangle.
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An isosceles triangle has at least two sides of equal length and two angles of equal measure.
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What is a scalene triangle?
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A scalene triangle is a triangle with all sides and all angles of different measures.
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Explain the exterior angle theorem.
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The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.
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How can you determine if three lengths can form a triangle?
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Three lengths can form a triangle if the sum of any two lengths is greater than the third length (triangle inequality theorem).
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What is an altitude in a triangle?
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An altitude is a perpendicular segment from a vertex to the line containing the opposite side or the extension of it.
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What is a median in a triangle?
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A median is a line segment joining a vertex to the midpoint of the opposing side, effectively dividing the triangle into two smaller triangles of equal area.
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What is an angle bisector in a triangle?
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An angle bisector divides an angle into two equal parts and in a triangle, it will meet the opposite side.
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Compare acute and obtuse triangles.
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An acute triangle has all three interior angles less than 90 degrees, while an obtuse triangle has one interior angle greater than 90 degrees.
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How do you find the perimeter of a triangle?
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The perimeter of a triangle is the sum of the lengths of its sides.
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What is Heron's formula for calculating the area of a triangle?
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Heron's formula is used to find the area of a triangle using its side lengths: √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter, or (a+b+c)/2.
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