Chapter 4 Flashcards
Define postulate 4.2 continuity postulate
If k is a half plane determined by line AC, then for every real number, 0<_ 180, there is exactly one ray, ray AB, that lies in k such that
m/_BAC=x
Define Postulate 4.1 protractor postulate
For every angle A there corresponds a positive real number less than or equal to 180. This symbolizes 0<_ 180
Postulate 4.3 angle addition postulate
If K lies in the interior of angle LMP, then
m/_ MNP=m/_MNK +m/_KNP
Theorem 4.1
All right angles are congruent
Theorem 4.2
If two angles are adjacent and supplementary, they form a linear pair
Theorem 4.3
Angles that form a linear pair are supplementary
Theorem 4.4
If one angle of a linear pair is a right angle, then the other angle is also a right angle
Theorem 4.5 vertical angle theorem
Vertical angles are congruent
Theorem 4.6
Congruent supplementary angles are right angles
Theorem 4.7 angle bisector theorem
If ray AB bisected angle CAD, them m/_ CAB = 1/2 m/_ CAB
A real number a is greater than a real number b (a>b) if
There is a positive real number c so that a=b+c
Define the measure of an angle
The real number that corresponds to a particular angle
Define congruent angles
Angles that have the same measure
Define slope of a line
A ratio obtained from two points of a line by dividing the difference of the y coordinates by the difference in x coordinates
Define adjacent angles
Are two coplanar angles that have a common side and a common vertex but no common interior points
Define an angle bisector
Is Ray that (except for its origin) is in the interior of an angle and forms congruent adjacent angles
Define perpendicular lines
Lines that intersect to form right angles
Define a linear pair
A pair of adjacent angles whose noncommon sides form a straight angle ( are opposite rays )
Define vertical angles
Angles adjacent to the same angle and forming linear pairs with it
Define complimentary angles
If the sum of the two angles is 90*
Define supplementary angles
If the sum of the two angles is 180*
Define acute triangle
Triangle with three acute angles
Define right triangle
A triangle with a right angle
Define obtuse triangle
A triangle with an obtuse angle
Define scalene triangle
A triangle with no congruent sides
Define isosceles triangle
A triangle with at least two congruent sides
Define equilateral triangle
A triangle with three congruent sides
Define trapezoid
A quadrilateral with a pair of parallel opposite sides
Define parallelogram
A quadrilateral with two pairs of opposite sides
Define rectangle
A parallelogram with four right angles
Define rhombus
A parallelogram with four congruent sides
Define square
A rectangle with four congruent sides (or a rhombus with four congruent angles)
