Theorems, Postulates, and Definitions Flashcards
Postulate:
How many lines run through 2 distinct points?
Through 2 distinct points, there is exactly one line.
Ruler postulate
The measure of any line segment is a unique positive number.
Segment-addition postulate
If X is a point of Line(AB) and A-X-B, then AX + XB = AB.
Postulate:
If 2 lines intersect, what do they intersect at?
If 2 lines intersect, they intersect at a point.
Postulate:
How many planes pass through 3 non-collinear points?
Through 3 non-collinear points, there is exactly one plane.
Postulate:
What appears at the intersection of 2 distinct planes?
If two distinct planes intersect, then their intersection is a line.
Postulate:
If there are 2 distinct points in a plane, what does that say about the line containing these points?
Given 2 distinct points in a plane, the line containing these points is also in the plane.
Theorem:
The midpoint of a line segment is …
Unique.
Protractor postulate
The measure of an angle is a unique positive number.
Angle-addition postulate
If a point D lies in the interior of an angle ABC, then m∠ABD + m∠DBC = m∠ABC
What are complementary angles?
Adjacent angles that add to 90 deg.
What are supplementary angles?
Adjacent angles that add to 180 deg.
Theorem:
How many bisector angles are there for a given angle?
There is one and only one angle bisector for a given angle.
Theorem:
2 perpendicular lines meet to form what kind of angles?
Right angles.
Theorem:
2 intersecting lines form what kind of vertical angles?
The vertical angles are congruent.
Theorem:
Given a plane, what can you say about a line perpendicular to a given line in that plane, at any point on that line?
There is exactly one line perpendicular to a given line in a plane at any point on that line.
Theorem:
What can you say about the perpendicular bisector of a line segment?
It’s unique.
Theorem:
If two angles are complementary to the same angle (or to congruent angles), then …
these angles are congruent.
Theorem:
If two angles are supplementary to the same angle (or to congruent angles), then …
these angles are congruent.
Theorem:
Any two right angles are …
congruent.
Theorem:
If the exterior sides of two adjacent acute angles form perpendicular rays, then …
these angles are complementary.
Theorem:
If the exterior sides of two adjacent angles form a straight line, then …
these angles are supplementary.
Theorem:
If two line segments are congruent, then …
their midpoints separate these segments into four congruent segments.
Theorem:
If two angles are congruent, then …
their bisectors separate these angles into four congruent angles.
