theorems chapter 5 Flashcards Preview

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Flashcards in theorems chapter 5 Deck (17):
1

perpendicular bisector thm

if a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

2

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.

3

angle bisector thm

if a point is on the bisector of an angle, then it is equidistant from the sides of an angle.

4

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.

5

circumcenter thm

the circumcenter of a triangle is equidistant from the vertices of the triangle

6

incenter thm

the incenter of a triangle is equidistant from the sides of the triangle.

7

centroid thm

the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.

8

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.

9

5-5-1

if two sides of a triangle are not congruent, then the larger angle is opposite the longer side.

10

5-5-2

if two angles of a triangle are not congruent, then the longer side is opposite the larger angle.

11

triangle inequality thm

the sum of any two side lengths of a triangle is greater than the third side length

12

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

13

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.

14

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

15

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

16

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

17

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