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# WHS Ch 5 - Triangles

### WHS Chapter 5 Properties/Attributes of Triangles

TermDefinition
acute triangle triangle with all three angles < 90°
right triangle triangle with one 90° angle
obtuse triangle triangle with one angle > 90°
angle bisector a line or ray that divides an angle into two congruent angles
conclusion the phrase following the word 'then' in a conditional statement
leg of a right triangle one of the two sides that form the right angle in a right triangle
perpendicular bisector of a segment a line that is perpendicular to a segment at its midpoint
altitude of a triangle a perpendicular segment from a vertex to the line containing the opposite side
centroid of a triangle the point of concurrency of the three medians of a triangle; also known as the center of gravity
circumcenter of a triangle the point of concurrency of the perpendicular bisectors of a triangle
concurrent three or more lines that intersect at one point
equidistant the same distance from two or more objects
incenter of a triangle the point of concurrency of the three angle bisectors of a triangle
median of a triangle a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
midsegment of a triangle a segment that joins the midpoints of two sides of the triangle
orthocenter of a triangle the point of concurrency of the three altitudes of a triangle
polygon a closed plane figure formed by three or more line segments
bisect cuts or divides something into two equal parts
slope the measure of the steepness of a line
intersection the set of points that two or more lines have in common
trinomial polynomial with 3 terms
equiangular triangle triangle with three equal measures
perimeter distance around a figure
deductive reasoning using logic to draw conclusions from facts, definitions, and properties
circumference distance around a circle
coplanar points in the same plane
translation movement across a plane
midsegment triangle the triangle formed by the three midsegments of a triangle
locus a set of points that satisfies a given condition
Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
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.
Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
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.
point of concurrency a point where three or more lines coincide
Circumcenter Theorem The circumcenter of a triangle is equidistant from the vertices of the triangle.
inscribed When a circle in a polygon intersects each line that contains a side of the polygon at exactly one point
circumscribed when a circle contains all the vertices of a polygon
Incenter Theorem The incenter of a triangle is equidistant from the sides of the triangle.
Centroid Theorem The centroid of a triangle is located ⅔ of the distance from each vertex to the midpoint of the opposite side.
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.
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".
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.
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.
Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the third side length.
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.
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.
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.
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.
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.
Created by: cawhite