Section 1
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Cards (104)
Section 1
(50 cards)
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
vertex of an angle
Definition: two angles whose sides are opposite rays. Or straight lines.
Side-Angle-Side (SAS) Postulate
If 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.
protractor
Definition: geometry tool used to measure angles Example: geometry tool used to measure angles
straight angle
formed by two opposite rays and measures 180 degrees
congruent segments
Definition: segments with the same length Example: Two segments of equal length. Shown by tick marks.
Linear Pair Postulate
Definition: If two angles form a linear pair, then they are supplementary and adjacent! Example: supplementary and adjacent angles
angle bisector
Definition: divides an angle into two congruent pieces Example: When an object or angle is able to be divided into two even halves. If you were to take 180 degrees and divide the total by 2, you then get 90 degrees.
Line
Definition: a straight path extending in opposite directions with no end. Contains infinitely many points. Example: straight path that goes in opposite directions and has an infinite number of points
Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent.
bisects
Definition: divides an item into two congruent pieces Example: When a ray divides an angle into two congruent pieces. ex. a 90 degree angle gets divided into two 45 degree angles
segment
part of a line the consists of two endpoints and all points in between.
Plane
represented by a flat surface that extends without end. Contains infinitely many lines.
hypotenuse
side opposite the right angle (aka the longest side)
obtuse angle
Definition: measures greater than 90 and less than 180 degrees Example: An angle which measures greater than 90 degrees and less than 180 degrees
isosceles triangle
has at least 2 congruent sides.
complementary angles
two angles whose measures have a sum of 90. Each angle is called the complement of the other.
Point
Definition: an object that indicates location. Has no size. Example: indicates a location that has no size
vertex angle (of an isosceles triangle)
Angle formed by the legs of an isosceles triangle.
ray
Definition: part of a line that consists of one endpoint and all points of the line on one side of the endpoint. Example: A ray is part of a line that extends in one direction indefinitely. A light ray is a real life example.
base (of an isosceles triangle)
side opposite the vertex angle in an isosceles triangle.
Third Angles Theorem
If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the third angles are congruent.
Side-Side-Side (SSS) Postulate
If the 3 sides of 1 triangle are congruent to the 3 sides of another triangle, then the 2 triangles are congruent.
midpoint
Definition: point that bisects the segment into two congruent segments Example: Point C is the midpoint of line segment AB.
adjacent angle
Definition: two coplanar angles with a common side, a common vertex, and no common interior points. Example: 2 coplanar angles with a common side , a vertex and no common interior points
included side
the common side of two consecutive angles in a polygon.
base angles (of an isosceles triangle)
2 angles that share a base as a side.
angle
Definition: formed by 2 rays that share the same endpoint Example: formed by 2 rays that share the same endpoint
If a triangle is equiangular,
then the triangle is equilateral.
colinear
Definition: on the same line Example: on the same line
complementary angles
two angles whose measures have a sum of 90. Each angle is called the complement of the other.
An equilateral triangle is
also equiangular
angle bisector
A ray that divides an angle into two congruent angles.
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent.
Hypotenuse Leg (HL) Theorem
If the hypotenuse and a leg of 1 right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
right angle
Definition: measures 90 degrees Example: An example of a right angle is a angle iron
Angle-Side-Angle (ASA) Postulate
If 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.
Congruent Polygons
Have corresponding parts congruent.
congruent angles
Definition: angles that have the same measure Example: Vertical angles
acute angle
Definition: angle that measures greater than 0 and less than 90 degrees Example: its an angle that measures smaller than 90 degrees but bigger than 0 degrees
vertical angles
Definition: two angles whose sides are opposite rays. Or straight lines. Example: Vertical angles are two angles whose sides are opposite rays. Or straight lines.A four way intersection.
supplementary angles
two angles whose measures have a sum of 180. Each angle is supplementary to the other.
3 Requirements to use the HL Theorem
1. There are 2 right triangles. 2. Triangles have congruent hypotenuses. 3. There is 1 pair of congruent legs.
sides of an angle
Definition: rays Example: Ray AB and ray AC are the sides of the angle BAC.
segment bisector
a point, line, ray, or other segment that intersects a segment at its midpoint
If a line bisects the vertex angle of an isosceles triangle,
then the line is also perpendicular to the base.
included angle
an angle formed by two adjacent sides of a polygon
legs
congruent sides of an isosceles triangle
Angle-Angle-Side (AAS or SAA) Postulate
If 2 angles and a nonincluded side of 1 triangle are congruent to 2 angles and corresponding nonincluded side of another triangle, then the triangles are congruent.
Plane
Definition: represented by a flat surface that extends without end. Contains infinitely many lines.
Section 2
(50 cards)
Theorem
any statement that you can prove.
Congruent Complements Theorem
If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
Reflexive Property of Equality
a = a
Inductive Reasoning
the process of reasoning that a rule or statement is true because specific cases are true.
Skew Lines
noncoplanar lines that are not parallel and do not intersect
alternate interior angles
angles that lie on opposite sides of the transversal and between the lines
|| (symbol)
means is parallel to
Converse of the Alternate Interior Angles Theorem
If 2 lines and a transversal form alternate interior angles that are congruent, then the lines are parallel.
vertex of an angle
endpoint where the 2 rays intersect
Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
Parallel Transitivity Theorem
If 2 lines are parallel to the same line, then they are parallel to each other.
Deductive Reasoning
the process of using logic to draw conclusions from given facts, definitions, and properties.
Exterior angles of a polygon
the angle formed by a side and an extension of a side
Parallel Lines
Coplanar lines that do not intersect.
corresponding angles
angles that lie on the same side of the transversal t, and the sames sides of the lines.
Converse of the Same-Side Interior Angles Theorem
If 2 lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel.
Addition Property of Equality
If a = b, then a + c = b + c.
Division Property of Equality
If a = b, then a/c = b/c.
Corresponding Angles Theorem
If a transversal intersects 2 parallel lines, then corresponding angles are congruent.
same-side interior angles (consecutive interior angles)
angles that lie on the same side of the transversal and between the lines.
Distributive Property
a(b+c) = ab + ac
Transitive Property of Equality
If a = b and b = c, then a = c.
Parallel Postulate
Through a point not on a line, there is one and only one line parallel to the given line.
Substitution Property
If a = b, then b can be substituted for a in any expression.
Subtraction Property of Equality
If a = b, then a - c = b - c.
Counterexample
an example where the conjecture is not true.
Converse of the Alternate Exterior Angles Theorem
If 2 lines and a transversal form alternate exteriorangles that are congruent, then the lines are parallel.
Vertical Angles Theorem
Vertical Angles are Congruent
Converse of the Corresponding Angles Theorem
If 2 lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
Supplementary Right Angles
If two angles are congruent and supplementary, then each is a right angle.
Multiplication Property of Equality
If a = b, then ac = bc.
segment
part of a line the consists of two endpoints and all points in between.
Same-Side Interior Angles Postulate
If a transversal intersects 2 parallel lines, then same side interior angles are supplementary.
Slope of a line
ratio of the vertical change (rise) to the horizontal change (run) between any two points.
alternate exterior angles
angles that lie on opposite sides of the transversal and outside of the lines.
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its 2 remote interior angles.
Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.
parallel planes
planes that do not intersect
Alternate Interior Angles Theorem (AIA)
If a transversal intersects 2 parallel lines, then alternate interior angles are congruent.
The unnamed Perpendicular-Parallel Theorem (Theorem 3.9)
In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.
straight angle
formed by two opposite rays and measures 180 degrees
transversal
line that intersects 2 coplanar lines at 2 different points.
Alternate Exterior Angles Theorem
If a transversal intersects 2 parallel lines, then alternate exterior angles are congruent.
Proof
a convincing argument using deductive reasoning, proving why a conjecture is true.
segment bisector
a point, line, ray, or other segment that intersects a segment at its midpoint
Remote interior angle
two nonadjacent interior angles corresponding to each exterior angle
supplementary angles
two angles whose measures have a sum of 180. Each angle is supplementary to the other.
Congruent Supplements Theorem
If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
Right Angles Theorem
All right angles are Congruent
Symmetric Property of Equality
If a = b, then b = a.
Section 3
(4 cards)