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Postulates, Theorems, and Constructions

Terms in this set (60)

Postulate 1-1
Through any two points there is exactly one line
Postulate 1-2
If two lines intersect, then they intersect in exactly one point
Postulate 1-3
If two planes intersect, then they intersect in exactly one line
Postulate 1-4
Through any three noncollinear points there is exactly one plane
Postulate 1-5 (Ruler Postulate)
Every point on a line can be paired with a real number
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC
Postulate 1-9
If two figures are congruent, then their areas are equal
Law of Detachment
If a conditional is true and its hypothesis is true, then its conclusion is true.
Law of Syllogism
when p->q is true, and q->r is true, then p->r is true
Vertical Angles Theorem
Vertical angles are congruent
Congruent Supplements Theorem
If two angles are supplements of the same angle, then the two angles are congruent.
Theorem 2-4
All right angles are congruent
Theorem 2-5
If two angles are congruent and supplementary, then each is a right angle.
Corresponding Angles Postulate
If a transversal intersects two parallel lines, then corresponding angles are congruent.
Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior angles are congruent.
Same-Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines, then same-side interior angles are supplementary.
Theorem 3-9
If two lines are parallel to the same line, then they are parallel to each other
Theorem 3-10
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Theorem 3-11
In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.
Triangle Exterior Angle Theorem
The measure of the exterior angle of a triangle is equal to the sum of its two remote interior angles.
Corollary to the Triangle Exterior Angle Theorem
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
Parallel Postulate
Through a point not on a line, there is one and only one line parallel to the given line.
Polygon Angle Sum Theorem
The sum of the interior angle measures of a convex polygon with n sides is (n-2)180
Polygon Exterior Angle Sum Theorem
The sum of the exterior angle measures, on angle at each vertex, of a convex polygon is 360 degrees.
Slopes of Parallel Lines
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope
slopes of perpendicular lines
Slopes are negative reciprocals of each other; their product should equal -1
Theorem 4-1
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Corollary to the Isosceles Triangle Theorem
If a triangle is equilateral, then the angles opposite those sides are congruent
Theorem 4-5
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
Hypotenuse Leg (HL) Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
Triangle Midsegment Theorem
A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
Theorem 5-6
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.
Theorem 5-8
The medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex.
Theorem 5-9
The lines that contain the altitudes of a triangle are concurrent.
Comparison Property of Inequality
If a=b+c and c>0, then a>b
Theorem 5-10
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Theorem 6-1
Opposite sides of a parallelogram are congruent.
Theorem 6-2
Opposite angles of a parallelogram are congruent
Theorem 6-3
The diagonals of a parallelogram bisect each other
Theorem 6-5
If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.
Theorem 6-6
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6-7
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 6-8
If one pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
Theorem 6-9
Each diagonal of a rhombus bisects two angles of the rhombus.
Theorem 6-11
The diagonals of a rectangle are congruent
Theorem 6-12
If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus
6-13
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus
6-14
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
6-15
The base angles of an isosceles trapezoid are congruent
6-16
the diagonals of an isosceles trapezoid are congruent
6-17
the diagonals of a kite are perpendicular
Trapezoid Midsegment Theorem
Trapezoid midsegment is parallel to bases and half the sum of the base lengths
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