Term
Parrallel Lines
Parrallel Planes |
|
Definition
Are coplanar lines that do not intersect.
Planes that do not intersect
Pg. 73 |
|
|
Term
|
Definition
Are noncoplanar lines, that are neither parallel or intersecting
Pg. 73 |
|
|
Term
A line and plane
are Parallel |
|
Definition
If they do not intersect
Pg. 73 |
|
|
Term
Theorem 3-1
If two ǁ planes are cut by a third plane, then _________ |
|
Definition
If two parallel planes are cut by a third plane, then the lines of intersection are parallel.
Pg. 74 |
|
|
Term
|
Definition
A line that intersects two or more coplanar lines in different points.
Pg. 74 |
|
|
Term
|
Definition
Two nonadjacent interior angles on opposite sides of the transversal.
Pg. 74 |
|
|
Term
Same-Side
Interior Angles |
|
Definition
Two interior angles on the same side of the transversal.
Pg. 74 |
|
|
Term
|
Definition
Two angles in corresponding positions relative to the two lines.
Pg. 74 |
|
|
Term
Postulate 10
Correspoinding <'s |
|
Definition
If two parallel lines are cut by a transversal, then correspoinding angles are congruent.
Pg. 78 |
|
|
Term
Theorem 3-2
Starting with ǁ lines |
|
Definition
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
Pg. 78 |
|
|
Term
Theorem 3-3
Starting with ǁ lines |
|
Definition
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Pg. 79 |
|
|
Term
Theorem 3-4
If a transversal is ┴ to one of two ǁ lines, then _______ |
|
Definition
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.
Pg. 79 |
|
|
Term
Postulate 11
Converse to corr. <'s (Post. 10) |
|
Definition
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Pg. 83 |
|
|
Term
Theorem 3-5
Starting with alt. int. <'s |
|
Definition
If two lines are cut by a transversal and alt. int. angles are congruent, then the lines are parallel.
Pg. 83 |
|
|
Term
Theorem 3-6
Starting with same-side int. <'s |
|
Definition
If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.
Pg. 84 |
|
|
Term
|
Definition
In a plane two lines are perpendicular to the same line are parallel.
Pg. 84 |
|
|
Term
|
Definition
Through a point outside a line, there is exactly one line paralllel to the given line.
Pg. 85 |
|
|
Term
|
Definition
Through a point outside a line, there is exactly one line perpendicular to the given line.
Pg. 85 |
|
|
Term
Theorem 3-10
Three ǁ lines |
|
Definition
Two lines parallell to a third line are parallel to each other.
Pg. 85 |
|
|
Term
Ways to Prove
Two Lines Parallel |
|
Definition
Show corr. <'s are ≅
Show alt. int. <'s are ≅
Show same-side int. <'s are supp.
Show both lines are ┴ to a third line
Show both lines are ǁto a third line.
Pg. 85 |
|
|
Term
|
Definition
The figure formed by three segments joining three noncollinear points.
Pg. 93 |
|
|
Term
Vertex & Sides
of a triangle |
|
Definition
Vertex - each of the three points of the triangle (Pluural: Vertices)
Sides - The segments of a triangle
Pg. 93 |
|
|
Term
|
Definition
|
|
Term
|
Definition
At least two sides congruent
Pg. 93 |
|
|
Term
|
Definition
All sides congruent
Can also be considered isosceles
Equilateral triangle is also equiangular
Pg. 93 |
|
|
Term
|
Definition
|
|
Term
|
Definition
One obtues <
A triangle can not have more then one obtuse <
Pg. 93 |
|
|
Term
|
Definition
One right <
A triangle can not have more than one right <
Pg. 93 |
|
|
Term
|
Definition
All <'s congruent
Equiangular triangles are also equilaterial
Pg. 93 |
|
|
Term
Theorem 3-11
Sum of the int. <'s of a ∆ |
|
Definition
The sum of the measure of the angles of a triangle is 180
Pg. 94 |
|
|
Term
Corollary 1, 2, 3 & 4
of Theorem 3-11 |
|
Definition
1. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent
2. Each angle of an equiangular triangle has measure 60
3. In a triangle, there can be at most one right angle or obtuse angle
4. The acute angles of a right triangle are complementary.
Pg. 94 |
|
|
Term
Theorem 3-12
Ext. < of a ∆ |
|
Definition
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
Pg. 95 |
|
|
Term
|
Definition
A line, ray, or segement added to a diagram to help in a proof.
Pg. 94 |
|
|
Term
|
Definition
Means "many angles". Any figure with three or more sides having the two qualitiles below.
1. Each segment intersects exactly two other segements, one at each endpoint
2. No two segments with a common endpoints are collinear
Pg. 101 |
|
|
Term
|
Definition
A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
Pg. 101 |
|
|
Term
|
Definition
3 Triangle 4 Quadrilateral
5 Pentagon 6 Hexagon
8 Octagon 10 Decagon
n n-gon
Pg. 101 |
|
|
Term
|
Definition
A segment joining two nonconsecutive vertices of a polygon.
Pg. 102 |
|
|
Term
Theorem 3-13
Sum of int. <'s of a polygon |
|
Definition
The sum of the measures of the angles of a convex polygon with n sides is (n-2)180
Pg. 102 |
|
|
Term
Theorem 3-14
Sum of ext. <'s of a polygon |
|
Definition
The sume of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.
Pg. 102 |
|
|
Term
|
Definition
A polygon that is both equiangluar and equlateral.
Pg. 103 |
|
|
Term
|
Definition
Conclusion based on accepted statements (definitions, postulates, previous theorems, corolaries, and given information)
Conclusion must be true if hypotheses are true.
Pg. 106 |
|
|
Term
|
Definition
Conclusion based on several past observations
Conclusion is probably true, but not necessarily true.
Pg. 106 |
|
|
