Topic 1: Properties of Triangles
Definitions:
Equilateral Triangle - A triangle with 3 equal sides.
Isosceles Triangle - A triangle with at least 2 equal sides.
Scalene Triangle - A triangle with no equal sides.
Equiangular Triangle - All angles are the same.
Acute Triangle - A triangle that contains 3 acute angles.
Right Triangle - a triangle that contains a right angle.
Obtuse Triangle - A triangle that contains an obtuse angle.
Triangle Angle Sum Theorem - The sum of the measures of the angles of a triangle is 180.
Exterior Angle - An angle formed by a side and an extension of an adjacent side.
Remote Interior Angles - The two nonadjacent angles.
Triangle Exterior Angle Theorem - The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
Equilateral Triangle - A triangle with 3 equal sides.
Isosceles Triangle - A triangle with at least 2 equal sides.
Scalene Triangle - A triangle with no equal sides.
Equiangular Triangle - All angles are the same.
Acute Triangle - A triangle that contains 3 acute angles.
Right Triangle - a triangle that contains a right angle.
Obtuse Triangle - A triangle that contains an obtuse angle.
Triangle Angle Sum Theorem - The sum of the measures of the angles of a triangle is 180.
Exterior Angle - An angle formed by a side and an extension of an adjacent side.
Remote Interior Angles - The two nonadjacent angles.
Triangle Exterior Angle Theorem - The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
Helpful Hints:
When classifying a triangle by its sides, it's either equilateral, isosceles, OR scalene.
When classifying a triangle by its angles, it's either acute, right, OR obtuse.
When classifying a triangle by its sides, it's either equilateral, isosceles, OR scalene.
When classifying a triangle by its angles, it's either acute, right, OR obtuse.
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Topic 2: Equilateral and Isosceles Triangles
Definitions:
Legs - The two congruent sides of an isosceles triangle.
Vertex Angle - The angle between the legs of an isosceles triangle.
Base - The third side of an isosceles triangle.
Base Angles - The two congruent angles of an isosceles triangle.
Isosceles Triangle Theorem - If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Corollary to the Isosceles Triangle Theorem - If a triangle is equilateral, then it is equiangular.
Legs - The two congruent sides of an isosceles triangle.
Vertex Angle - The angle between the legs of an isosceles triangle.
Base - The third side of an isosceles triangle.
Base Angles - The two congruent angles of an isosceles triangle.
Isosceles Triangle Theorem - If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Corollary to the Isosceles Triangle Theorem - If a triangle is equilateral, then it is equiangular.
Helpful Hints:
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Topic 3: Inequalities in Triangles
Definitions:
Triangle Inequality Theorem - two sides of a triangle, when added up, must be larger than the third side.
The largest angle is across from the largest side. (the reverse is also true)
The smallest angle is across from the smallest side. (the reverse is also true)
Triangle Inequality Theorem - two sides of a triangle, when added up, must be larger than the third side.
The largest angle is across from the largest side. (the reverse is also true)
The smallest angle is across from the smallest side. (the reverse is also true)
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Topic 4: Medians, Midsegments, and Altitudes
Definitions:
Midsegment (of a triangle) - a segment connecting the midpoints of two sides of the triangle.
Median (of a triangle) - a segment whose endpoints are a vertex and the midpoint of the opposite side.
Altitude (of a triangle) - the perpendicular segment from a vertex to the opposite side. It can be inside or outside the triangle, or it can be a side.
Midsegment (of a triangle) - a segment connecting the midpoints of two sides of the triangle.
Median (of a triangle) - a segment whose endpoints are a vertex and the midpoint of the opposite side.
Altitude (of a triangle) - the perpendicular segment from a vertex to the opposite side. It can be inside or outside the triangle, or it can be a side.
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