Midterm Review: Topic and Definitions
Chapter 1 Main Topics:
1.1: Points, Lines and Planes
1.2: Segments and Rays
1.3: Distance and Midpoint Formulas
1.4: Angles
1.5: Parallel and Perpendicular Lines
Define and give an example:
Point: Object that does not have an actual size
Line: Extend indefinitely and have no thickness or width
Collinear Points: Points that lie on the same line
Plane: a flat surface that extends indefinitely in all directions
Intersection: the set of points that is common for two given figures
Coplanar: Objects that lie on the same plane
Segment: part of a line that consists of two endpoints and all of the points in between
Segment Addition Postulate: If C is between A and B, then AC + CB = AB
Congruent Segments: Segments with equal lengths
Ray: part of a line, has one fixed endpoint, and extends infinitely along the line from the endpoint.
Opposite Rays: rays with a common endpoint, extending in opposite directions and forming a line.
Distance Formula:
Midpoint Formula:
Bisector: the line that divides something into two equal parts
Angle: a figure formed by two rays with a common endpoint
Vertex: common endpoint of an angle
Acute Angle: an angle whose measure is less than 90 degrees
Right Angle: an angle whose measure = 90 degrees
Obtuse Angle: an angle whose measure is bigger than 90 degrees but less than 180 degrees
Straight Angle: an angle that is 180 degrees
Angle Addition Postulate: The sum of two parts of an angle will equal the whole angle
Congruent Angles: two angles with the same measurement
Angle Bisector: a ray in the interior of the angle that divides the angle into two congruent angles
How to find slope of a graph:
How to find slope of ordered pairs:
Parallel Equations: two equations that have the same slope and different y-intercepts; their graphs will never intersect
Perpendicular Equations: The equations have slopes that are opposite reciprocals; their graphs cross to form a right
angle
Opposite Reciprocals: two numbers that have opposite signs and are flipped fractions of each other.
Chapter 3 Main Topics:
3.1: Angle Relationships
3.2: Identify Pairs of Lines and Angles
3.3a: Angles and Parallel Lines
3.3b: Proving Lines Parallel
Define and give an example:
Complementary angles: When two angles add up to 90 degrees
Supplementary angles: When two angles add up to 180 degrees
Adjacent angles: two angles that share a common vertex and side but have no common interior points
Linear Pair: two adjacent angles that are supplementary
Vertical angles: a pair of angles whose sides form opposite rays
Corresponding angles: pairs angles that have corresponding locations when two lines are cut by a transversal
Alternate interior angles: pairs of angles in the interior on opposite sides of the transversal
Alternate exterior angles: pairs of angles in the exterior of two lines cut by a transversal on opposite sides
Consecutive interior angles: pairs of interior angles on the same side of the transversal
Transversal: a line that intersects two or more lines in a plane at different points
Chapter 4 Main Topics:
4.1: Intro to Triangles
4.2: Congruent Triangles
4.3: Isosceles Triangles
4.4: Triangle Inequalities
Define and give an example:
Acute triangle: triangle with three acute angles
Right triangle: triangle with one right angle. The other two angles are acute and complementary
Obtuse triangle: triangle with one obtuse angle
Equiangular triangle: triangle with three congruent angles
Isosceles triangle: a triangle with at least two congruent sides
Scalene triangle: a triangle with no congruent sides
Equilateral triangle: a triangle with all congruent sides
Isosceles triangle theorem: If two sides of a triangle are congruent, then the angles opposite of them are also congruent
Legs in an isosceles triangle: The two congruent sides
Base angles in an isosceles triangle: The two congruent angles
Base of an isosceles triangle: the side that is formed by the two base angles
Chapter 5 Main Ideas
5.1: Proving Triangles Congruent
5.2: Using Proofs with Triangles
Define:
CPCTC: corresponding parts of congruent triangles are congruent
Name the 5 congruent triangle postulates: SSS, SAS, AAS, ASA, HL
Reflexive property: any quality equal to itself
Symmetric property: if one quantity is equal to a 2nd quantity, then the 2nd quantity is equal to the first
Chapter 6 Main Ideas:
6.1: Similar Polygons
6.2: Proving Triangles Similar Through AA
6.3: Mid-segment of a Triangle
6.4: Partitioning a Line Segment
Define:
Similar figures: two polygons are similar iff their corresponding angles are congruent and lengths of corresponding sides
are proportional
Proportional: lengths of sides are proportional iff the ratios of the lengths of corresponding sides are equal
Scale factor: The ratio of corresponding sides of similar polygons
AA Similarity: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar
Mid-segment of a triangle: a segment joining the midpoints of two sides of a triangle
Property 1 of a mid-segment: a mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is
parallel to the third side of the triangle
Property 2 of a mid-segment: the mid-segment of a triangle joins the midpoints of two sides of a triangle such that its
length is half the length of the third side of the triangle