Chapter 1 Vocab, Postulates and Theorems
Types of angles:
Acute
Right
Obtuse
Straight
Adjacent angles: angles that share a vertex and a ray
Angle bisector: a line, ray, or segment, that goes through the midpoint of a segment
Collinear points: two or more points that are on the same line
Coplanar points: two or more points that lie on the same plane
Complementary angles: angles whose measures sum to 90
Congruent angles: angles that have the same measure
Congruent segments: segments that have the same length/measure
Linear pair: a pair of supplementary adjacent angles that make a straight angle
Perpendicular Bisector: a line that intersects a segment at its midpoint, creating a right angle
Perpendicular Lines: two lines whose intersection create a right angle
Point: (dot)
Line: goes through at least two points in both directions forever (and ever…)
Midpoint: divides the segment into two congruent segments
Plane: a flat surface that includes at least three points and extends in all directions without end
Ray: starts at a single point and goes in one direction forever (include a second point)
Opposite rays: start at a single point and go in opposite directions forever
Segment: part of a line that has two endpoints (does not go on forever)
Segment bisector: a line, ray, or segment that goes through the midpoint of a segment, splitting the
segment into two congruent parts
Supplementary angles: two angles whose measures add up to 180 degrees
Vertex of an angle: the point that the rays start at when making an angle
Vertical angles: two angles whose sides are opposite rays and share a common vertex
𝑥1 +𝑥2
2
Midpoint Formula = (
,
𝑦1 +𝑦2
)
2
Distance Formula = √(𝑦2 − 𝑦1 ) + (𝑥2 − 𝑥1 )
Area and Perimeter:
Square
Rectangle
Triangle
Circle
𝑃 = 4𝑠
𝑃 = 2𝑏 + 2ℎ
𝑃 =𝑎+𝑏+𝑐
𝐶 = 2𝜋𝑟
𝐴 = 𝑠2
𝐴 =𝑙∗𝑤
𝐴=
1
𝑏
2
∗ℎ
𝐴 = 𝜋𝑟 2
Chapter 2 Vocab
Biconditional: if and only if statement
Conclusion: the part of the statement that follows: then
Conditional: if-then statement
Conjecture: a conclusion you reach using inductive reasoning (educated guess)
Contrapositive: negate the hypothesis and the conclusion of the converse (~𝑞 → ~𝑝)
Converse: switch the hypothesis and the conclusion of the conditional (𝑞 → 𝑝)
Counterexample: an example that shows a conjecture is incorrect
Deductive Reasoning: using logic from given statements to reach a conclusion
Hypothesis: In an if-then statement, the part that follows the: if
Inductive Reasoning: a type of reasoning that reaches conclusions based on patterns or past events
Inverse: ~𝑝 → ~𝑞
Law of Detachment: If 𝑝 → 𝑞 is true and 𝑝 is true, then 𝑞 is true.
Law of Syllogism: If 𝑝 → 𝑞 is true and 𝑞 → 𝑟 is true, then 𝑝 → 𝑟 is true.
Negation: the opposite of a given statement; also used in the form of ~
Paragraph proof: a proof with statements and reasons organized in sentences
Proof: a convincing argument that uses deductive reasoning
Theorem: a conjecture that is proven
Truth Value: the identification of a statement which is either true or false
Chapter 3 Vocab
Alternate Exterior Angles: two angles that are formed by two lines and a transversal and that lie outside
the two lines on opposite sides of the transversal
Alternate Interior Angles: nonadjacent interior angles that lie on opposite sides of the transversal
Corresponding Angles: angles that lie on the same side of the transversal and in corresponding positions
Exterior Angles of a Polygon: an angle formed by a side and an extension of an adjacent side
Flow Proof: a proof structured with arrows to show the logical flow of reasoning
Parallel Lines: two lines in the same plane that do not intersect
Parallel Planes: planes that do not intersect
Point-Slope Form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
Remote Interior Angles: the two nonadjacent interior angles corresponding to each exterior angle of a
triangle
Same-Side Interior Angles: angles that lie on the same side of the transversal and between the two lines
Skew Lines: lines that do not touch and do not lie in the same plane
𝑟𝑖𝑠𝑒 𝑦 −𝑦
Slope: 𝑟𝑢𝑛 ; 𝑥2 −𝑥1
2
1
Slope-intercept Form: 𝑦 = 𝑚𝑥 + 𝑏
Transversal: a line that intersects two or more lines at distinct points
Chapter 4 Vocab
Base Angles of an Isosceles Triangle: the two congruent angles opposite the congruent sides
Base of an Isosceles Triangle: the third side of an isosceles triangle that is not necessarily congruent
Congruent Parts of Congruent Triangles are Congruent: After proving that two triangles are congruent,
we can use this to prove that any two angles or segments that correspond in the two triangles are
congruent to each other.
Congruent Polygons: two figures that have all corresponding sides and angles congruent
Congruent Triangle Postulates/Theorems
SSS
SAS
ASA
AAS
Corollary: a theorem that can be proved easily using another theorem
Equilateral Triangle: a three sided figure with all three sides congruent
Hypotenuse: in a right triangle, the side opposite the right angle (or just the longest side)
Isosceles Triangle: a three-sided figure with two or more sides congruent
Legs of an Isosceles Triangle: the two or more congruent sides in an isosceles triangle
Legs of a Right Triangle: the two sides that create a 90-degree angle in a right triangle
Vertex of an Isosceles Triangle: the angle created by the two congruent sides
HL