Final Exam Flashcards
What is the box or pigeon hole principle?
If you have more marbles than boxes and each marble must go in a box, then at least 1 box has multiple marbles.
What is a point?
A singular location with no size, is infinitely small, has no dimensions. It is named with capital letters.
What is a line?
A “moving point”, it travels in two opposite directions forever. It is one dimensional, named by 2 points, never bends or curves, and is infinitely thin.
What is a plane?
A infinitely short/flat/thin surface that spans outward in all directions. It is named with 3 points.
What is a segment or line segment?
A “line” that starts out at one point and ends at another. Or a part of a line formed between two points.
What is a ray?
A “line” that extends in one direction forever. Or a part of a line that has one endpoint.
What is an angle?
2 rays with a common endpoint.
What are collinear points?
2 or more points that are on the same line.
What are coplanar points?
2 or more points on the same plane.
(Postulate)Two lines intersect to form a….
Point.
(Postulate)Two planes intersect to form a……
Line.
(Postulate)Through any two points there is exactly one…..
Line.
(Postulate)Through any 3 non-collinear points there is exactly one…..
Plane.
(Postulate)If you take two points in a plane, then the line containing those points must…..
Be on the same plane
What is inductive reasoning?
Reaching conclusions based on observations.
What is a sequence?
A list of numbers.
What is a term?
A number in the list?
What is an arithmetic sequence?
A sequence where you add/subtract the same number between consecutive terms.
What is a geometric sequence?
A sequence where you multiply by the same number between consecutive terms.
What are congruent segments?
2 segments having the same length.
What is a midpoint?
A point splitting a segment into 2 congruent segments.
What is the segment addition postulate?(SAP)
The distance from A to B and B to C is equal to the distance from A to C. (Part+Part=Whole)
What are complementary angles?
2 angles that add up to 90 degrees.
What are supplementary angles?
2 angles that add up to 180 degrees.
What are the three types of angles?
- Acute(below 90)
- Right(90)
- Obtuse(Above 90)
What are congruent angles?
2 angles with equal measures.
What is an angle bisector?
A ray that splits an angle into two congruent angles.
What are adjacent angles?
Two angles that:
- Have the same vertex
- Share a ray
- Dont overlap
What is a linear pair of angles?
2 adjacent angles that form a line.
What is the angle addition postulate?(AAP)
AVB+BVC=AVC.(Part+Part=Whole)
What is a median?
A line segment involving a triangle going from a vertex to the midpoint of the opposite side.
What is a centroid?
The point where the 3 medians of a triangle intersect.
What are the special properties of a centroid?
- Center of balance/gravity/mass
2. Centroid splits the medians into a 1/3 to 2/3 ratio
What is an altitude?
A segment involving a triangle going from a vertex perpendicular to the opposite side.
What is an orthocenter?
The point where the three altitudes of a triangle intersect.
What are parallel lines?
2 lines on the same plane that never intersect.
What are perpendicular lines?
2 lines that intersect to form a right angle.
What is a perpendicular bisector?
A line that intersects another line segment at its midpoint.
What is an incenter?
Thw point where the 3 angle bisectors of a triangle intersect.
What is an inscribed circle?
The circle centered at the incenter of a triangle that fits in the triangle perfectly.
What is the circumcenter?
The point where 3 perpendicular bisectors of a triangle intersect.
What is a circumscribed circle?
The circle centered at the circumcenter of a triangle that fits outside the triangle perfectly.
What is a conditional statement?
A sentence in if(hypothesis,p) then(conclusion) form that can be viewed as true or false.
What is a counterexample?
A reason why a statement is false.
What is a converse?
If p then q becomes if q then p.
What is the inverse?
If p then q becomes if not p then not q.
What is the contrapositive?
If p then q becomes if not q then not p.
What property is..
If a=b then a+c=b+c?
Addition
What property is….
If a=b then a-c=b-c?
Subtraction
What property is….
If a=b then ac=bc
Multiplication
What property is….
If a=b then a/c=b/c if c is not equal to zero?
Division
What property is
a(b-c)?
Distributive
What property is…
a=a?
Reflexive
What property is…..
if a=b then b=a
Symmetric
What property is…..
If a=b and b=c then a=c?
Transative
What property is….
if a=b then a and b can be used interchangably?
Substitution
What are the three properties of congruence?
- Reflexive
- Symmetric
- Transative
What is deductive reasoning?
Using logic, facts, and general principles to reach an indisputable conclusion.
What is a proof?
A step by step process using deductive reasoning to show why something must be true.
What are acceptable reasons in proofs?
- Given
- Definitions
- Properties
- Postulates
- Previously proven theorems
What are vertical angles
Pairs of angles formed by intersecting lines that are not adjacent.
What is the vertical angles theorem?(VAT)
If angles are vertical, they are congruent.
What is the overlapping angles theorem?(OST)
If AB=CD the AC=CD. If two congruent segments have the same overlapping segment, then the two larger overlapping segments are congruent.
What is the overlapping angles theorem?(OAT)
If AVB=CVD the AVC=BVD. If two congruent angles share the same overlapping angles, then the two larger overlapping angles are congruent.
What is a transversal?
A line that intersects two coplanar lines at different points.
What are interior angles?
Angles formed by a transversal that are “between” the coplanar lines.
What are exterior angles?
Angles formed by a transversal that are outside the coplanar lines.
What are corresponding angles?
Pairs of angles formed by a transversal that:
- have different vertices
- One is interior, one is exterior
- On the same side of the transversal
What are alternate interior angles?
Pairs of angles formed by a transversal that:
- Have different vertices
- Both are interior angles
- Not on the same side of the transversal
What are same side interior angles?
Pairs of angles formes by a transversal that:
- Have different vertices
- Are interior angles
- Are on the same side of a transversal
What are alternate exterior angles?
Pairs of angles formed by a transversal that:
- Have different vertices
- Both are exterior angles
- On different sides of the transversal
What is the corresponding angles postulate?(CAP)
If a transversal cuts two lines that the corresponding angles are congruent, then the lines are parallel.
What is the alternate interior angles theorem?(AIAT)
If a transversal cuts the two lines so that the alternate interior angles are congruent, then the line is parallel.
What is the same-side interior angles theorem?(SSIAT)
If a transversal cuts two lines so that the same-side interior angles are supplementary, then the lines are parallel.
What is the alternate exterior angles theorem?(AEAT)
If a transversal cuts two lines so that the alternate exterior angles are congruent, then the lines are parallel.
What is the converse of the angles postulate?(CCAP)
If a transversal cuts two parallel lines, then the corresponding angles are congruent.
What is the converse of the alternate interior angles theroem?(CAIAT)
If a transversal cuts two parallel lines, then the alternate interior angle pairs are congruent.
What is the converse of the same-side interior angles theorem?
If a tranversal cuts two parallel lines, then the same side interior angle pairs are supplementary.
What is the converse of the alternate exterior angles theorem?
If a transversal cuts two parallel lines, then the alternate exterior angle pairs are congruent.
What are remote interior angles?
In a triangle, the interior angles that are not adjacent to adjacent to a given exterior angle.
What is the triangle exterior angles theorem?
In any triangle, the measure from an exterior angle is equal to the sum of the measures of its remote interior angles.
What is the polygon exterior angles theorem?
In any polygon, the sum of the measures of a set of exterior angles in 360.
What is the parallel postulate?
Given any line and a point not on the line, there is a line parallel to the given line through the given point.
What is a polygon?
A connected set of at least three coplanar line segments such that each segment only intersects two others, one at each midpoint.
What is a triangle?
A three sided polygon.
What are interior angles of polygons?
Angles inside a polygon which are formed by two adjacent sides of the polygon.
What are exterior angles of polygons?
An angle outside a polygon which is formed by extending the side of the polygon.
How are the angle of depression and angle of elevation related?
They are congruent to each other.
What is the definition of similar polygons?
Two polygons are similar if one is a dilation of the other.
What are the criteria for polygons to be congruent?
Two polygons are similar if and only if there is a correspondance such that:
- Matching sides have to have the same ratio/scale factor
- Matching angles are congruent
What is the center of a regular polygon?
The center of its circumscribed circle.
What is the apothem?
A line segment going from the center of a regular polygon perpendicular to a side.
What is the definition of a circle?
A set of points equidistant from a given centerpoint.
What is a tangent line of a circle?
A line intersecting the circle exactly one time.
What is a point of tangency?
The point where a tangent line intersects a circle.
What is a radius?
A segment going from the center of a circle to a point on the circle.
What are congruent circles?
2 circles with congruent radii.
What are concentric circles?
Circles with the same centerpoint.
What is a chord?
A line segment with both endpoints on the circle.
What is diameter?
A chord going through the center of a circle.
What is a secant line?
A line intersecting a circle twice.
What is a central angle?
An angle whos vertex is at the center of a circle.
What is an inscribed angle?
An angle inside of a circle whose vertex is on the circle.
What is an arc?
Part of a circle.
What is a major arc?
An arc that is more han half of a circle.
What is a minor arc?
An arc that is less than half of a circle.
What is a semicircle?
Half of a circle.
What is the chord-chord power theorem?
If two chords of a circle intersect inside the circle, then the product of the measures of the segments is equal to the product of the measures of the segments of the other chord.
What is the secant-secant power theorem?
If two secant segments are drawn from a point outside a circle, then the product of the measures of one entire secant segment with its outside oart is equal to the product of the other secant segment with its outside part.
What are the pyrhagorean triples?
3-4-5
5-12-13
8-15-17
7-24-25
What is formed if you draw a radius from the center of a circle to the point of tangency?
Two 90 degree angles are formed.
Tangent segments to a circle from a point outside the circle are….?
Congruent.
What is surface area?
The combined area of all face or sides of a 3-d figure.
What volume and its formula?
V=Bh
Volume is how mucn capacity a 3-d object has inside.
What is Cavalieri’s principle?
Volume doesnt change based of how a figure is “stacked”
Example: Stack of pennies
What is the formula for volume of a pyramid or cone?
V=1/3•Bh
What is the formula for surface area of a cylinder?
2•pi•r(squared)+2•pi•r•h
What is the formula for volume of a sphere?
4/3•pi•r(CUBED)
What is the formula for surface area of a sphere?
4•pi•r(squared)
What is correspondence?
A way to pair two points between two polygons.
What is the polygon congruence postulate?(PCP)
Two polygons are congruent if and only if there is a correspondence between them such that:
- All pairs of corresponding sides are congruent
- All pairs of corresponding angles are congruent.
What is the triangle inequality theorem?
For a triangle to be formed, the sum of the legs of the two sides must be greater than the 3rd for all
possible arrangements.
What is a parallelogram?
A quadrilateral that has two pairs of parallel sides.
What is a rectangle?
A quadrilateral with four right angles.
What is a rhombus?
A quadrilateral with four congruent sides.
What is a square?
A quadrilateral with four right angles and four congruent sides.
What is a kite?
A quadrilateral with two pairs of congruent, adjacent, sides and its opposite sides are not congruent.
What is a transformation?
The process of moving a figure in a plain.
What is a preimage?
An image before it’s moved.
What is an image?
An image after it’s been moved.
What is a rigid transformation?
A transformation that preserves the size and shape of a figure.
What is an isosceles triangle?
A triangle with at least two congruent sides.
What is an equilateral triangle?
A triangle with three congruent sides.
What is an equilateral polygon?
A polygon with all sides congruent.
What is an equiangular polygon?
A polygon with all angles congruent.
What is a quadrilateral?
A four sided polygon.
What js a trapezoid?
A quadrilateral with EXACTLY one pair of parallel sides.
What does concurrent mean?
Multiple lines intersect at the same point.
