theorems chapter 5 Flashcards
(17 cards)
perpendicular bisector thm
if a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
converse of the perpendicular bisector thm
if a point is equidistant from the endpoints of a segment,, then it is on the perpendicular bisector of a segment.
angle bisector thm
if a point is on the bisector of an angle, then it is equidistant from the sides of an angle.
converse of angle bisector thm
if a point in the interior of an angle is equidistant from the sides of an angle, then it is on the bisector of an angle.
circumcenter thm
the circumcenter of a triangle is equidistant from the vertices of the triangle
incenter thm
the incenter of a triangle is equidistant from the sides of the triangle.
centroid thm
the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.
triangle mid-segment thm
a mid segment of a triangle is parallel to a side of a triangle, and its length of the opposite side.
5-5-1
if two sides of a triangle are not congruent, then the larger angle is opposite the longer side.
5-5-2
if two angles of a triangle are not congruent, then the longer side is opposite the larger angle.
triangle inequality thm
the sum of any two side lengths of a triangle is greater than the third side length
hinge thm
if two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle
converse of the hinge thm
if two sides of one triangle are congruent to two sides of another triangle and the third sides are not congruent, then the larger included angle is across from the longer third side.
converse of the pythagorean thm
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 thm
in triangle ABC, c is the length of the longest side. if c^2 > a^2 + b^2, then triangle ABC is obtuse. if c^2< a^2 + b^2, then triangle ABC is acute
45-45-90 triangle thm
in a 45-45-90 triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2
a= 2 b= 2 c= 2* square root of 2
30-60-90 triangle thm
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 of the square root of 3
a= 2
b= 2 * square root of 3
c=2 *2
