WHS Chapter 5 Properties/Attributes of Triangles
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| acute triangle | triangle with all three angles < 90°
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| right triangle | triangle with one 90° angle
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| obtuse triangle | triangle with one angle > 90°
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| angle bisector | a line or ray that divides an angle into two congruent angles
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| conclusion | the phrase following the word 'then' in a conditional statement
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| leg of a right triangle | one of the two sides that form the right angle in a right triangle
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| perpendicular bisector of a segment | a line that is perpendicular to a segment at its midpoint
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| altitude of a triangle | a perpendicular segment from a vertex to the line containing the opposite side
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| centroid of a triangle | the point of concurrency of the three medians of a triangle; also known as the center of gravity
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| circumcenter of a triangle | the point of concurrency of the perpendicular bisectors of a triangle
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| concurrent | three or more lines that intersect at one point
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| equidistant | the same distance from two or more objects
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| incenter of a triangle | the point of concurrency of the three angle bisectors of a triangle
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| median of a triangle | a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
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| midsegment of a triangle | a segment that joins the midpoints of two sides of the triangle
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| orthocenter of a triangle | the point of concurrency of the three altitudes of a triangle
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| polygon | a closed plane figure formed by three or more line segments
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| bisect | cuts or divides something into two equal parts
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| slope | the measure of the steepness of a line
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| intersection | the set of points that two or more lines have in common
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| trinomial | polynomial with 3 terms
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| equiangular triangle | triangle with three equal measures
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| perimeter | distance around a figure
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| deductive reasoning | using logic to draw conclusions from facts, definitions, and properties
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| circumference | distance around a circle
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| coplanar | points in the same plane
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| translation | movement across a plane
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| midsegment triangle | the triangle formed by the three midsegments of a triangle
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| locus | a set of points that satisfies a given condition
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| Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
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| Converse of the Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
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| Angle Bisector Theorem | If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
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| Converse of the Angle Bisector Theorem | If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.
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| point of concurrency | a point where three or more lines coincide
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| Circumcenter Theorem | The circumcenter of a triangle is equidistant from the vertices of the triangle.
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| inscribed | When a circle in a polygon intersects each line that contains a side of the polygon at exactly one point
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| circumscribed | when a circle contains all the vertices of a polygon
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| Incenter Theorem | The incenter of a triangle is equidistant from the sides of the triangle.
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| Centroid Theorem | The centroid of a triangle is located ⅔ of the distance from each vertex to the midpoint of the opposite side.
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| Triangle Midsegment Theorem | A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side.
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| indirect proof | Begin by assuming that the conclusion is false. Then show that this assumption leads to a contradiction. Also known as a "proof by contradiction".
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| Angle-Side Relationships in Triangles - Theorem 1 | If two sides of a triangle are not congruent, then the larger angle is opposite the longer side.
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| Angle-Side Relationships in Triangles - Theorem 2 | If two angles of a triangle are not congruent, then the longer side is opposite the larger angle.
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| Triangle Inequality Theorem | The sum of any two side lengths of a triangle is greater than the third side length.
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| Pythagorean Theorem | In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
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| Converse of the Pythagorean Theorem | If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
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| Pythagorean Inequalities Theorem | In ∆ABC , 'c' is the longest side. If c² > a² + b², the ∆ABC is an obtuse triangle. If c² < a² + b², then ∆ABC is an acute triangle.
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| 45°-45°-90° Triangle Theorem | In a 45°-45°-90° triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times √2.
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| 30°-60°-90° Triangle Theorem | In a 30°-60°-90° triangle, the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is the length of the shorter leg times √3.
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