9 Math Honors Sem 1 Midterms Study Set

Basic Terminology - 96 terms

point

a location with no dimensions

line

infinite stack of points placed end to end, no width no height

plane

a flat one-dimensional surface extending infinitely in all directions

segment

a part of a line between two points

coplanar

in the same plane

collinear

series of points lying in the same straight line

ray

a part of a line consisting of a point and all points on one side of it

conditional statement

an IF-THEN statement

hypothesis

the phrase between “if” and “then”

conclusion

the phrase after “then”

converse

swaps the hypothesis and the conclusion

inverse

negate both the hypothesis and the conclusion

contrapositive

switch the hypothesis and conclusion and negate both

angle

the figure formed by two rays with the same endpoint

sides of angle

the rays

vertex/vertices

the endpoint

intersecting lines

if two distinct lines intersect, it is at exactly one point

skew lines

noncoplanar lines that don’t intersect and aren't parallel

endpoint

a point that defines where a line segment stops

midpoint

a point that divides a segment into two congruent segments

bisector

line/ray/segment that intersects a midpoint

complementary angles

two angles whose measures have a sum of 90 degrees

supplementary angles

two angles whose measures have a sum of 180 degrees

linear pair

two adjacent angles formed by two intersecting lines/rays/segments

adjacent angles

two angles that share a common vertex, share a common side, and do not overlap

vertical angles

two non-adjacent angles formed by two intersecting lines

right angle

angle measuring 90 degrees

acute angle

0 degrees<x<90 degrees

obtuse angle

90 degrees<x<180 degrees

right triangle

1 right angle and 2 acute angles

acute triangle

3 acute angles

obtuse triangle

1 obtuse angle

scalene triangle

0 congruent sides

equilateral triangle

3 congruent sides

coordinates

x and y of a point on a coordinate plane

origin

the central point where the x and y-axis intersect

base angles

angles opposite the congruent sides

vertex angle

the angle where the two sides connecting to the vertex are congruent

isosceles triangle

a triangle with 2 congruent sides

x-axis

the horizontal axis of a coordinate plane

y-axis

the vertical axis of a coordinate plane

transformation

a process by which a geometric figure is moved or changed

translation

moves a figure a fixed distance in a given direction

reflection

each point of the pre-image has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line

rotation

transformation that turns a figure about a fixed point called the center of rotation.

angle of rotation

rays drawn from the center of rotation to a point and its image form an angle

line of symmetry

a transformation that can be applied to the figure to map it onto itself

rotational symmetry

order x angle = 360 degrees

reflectional symmetry

when you reflect a figure over a line on a shape and it reflects onto itself

image

ending point/shape

pre-image

starting point/shape

postulate

a mathematical proposition that we assume is true

theorem

a mathematical proposition that is definitely true and proven

parallel lines

two lines that are coplanar and don’t intersect

perpendicular lines

intersecting lines forming a right angle

transversal

a line that intersects 2 or more other lines

same side interior angles

pairs of angles formed when a transversal line cuts across two other lines. they are located inside the two lines and on the same side of the transversal. if lines are parallel, then they are supplementary.

alternate interior angles

pairs of angles on opposite sides of a transversal line, located between the two other lines it intersects. if lines are parallel, they are always congruent

alternate exterior angles

pairs of angles on opposite sides of a transversal line, located between the two other lines it intersects. if lines are parallel, they are always congruent.

corresponding angles

pairs of angles in the same relative position at each intersection where a transversal line cuts across two other lines

degrees

a unit for measuring angles

quadrilateral

4 sided polygon

pentagon

5 sided polygon

hexagon

6 sided polygon

septagon/heptagon

7 sided polygon

octagon

8 sided polygon

nonagon

9 sided polygon

decagon

10 sided polygon

dodecagon

12 sided polygon

polygon

a straight-sided plane figure with at least three sides and angles, and typically five or more

regular polygon

an equilateral, equiangular polygon

midsegment

the midpoints of two sides of a triangle that form a segment. parallel to the base.

median

a segment that connects a vertex of a triangle to the midpoint of the opposite sides

altitude

a segment that is perpendicular to a side of a triangle and intersects with the vertex opposite that side

perpendicular bisector

a line/segment that passes through the midpoint of a side of a triangle and is also perpendicular to that side

angle bisector

a line/segment that bisects an angle of a triangle and intersects the opposite side of the triangle

order (symmetry)

the number of times a shape looks like itself when doing a full 360-degree rotation

perimeter

total distance around the outside boundary of a 2-D shape

CS+CS are congruent

congruent segments added to congruent segments are congruent

CA+CA are congruent

congruent angles added to congruent angles are congruent

congruent

geometric elements that are the same size and same shape

CPCTC

corresponding parts of congruent triangles are congruent

Included angle

the angle formed at the vertex where two specific sides (or line segments) of a shape, like a triangle or polygon, meet

included side

the side of a polygon that lies directly between two consecutive angles, connecting their vertices

hypotenuse

the longest side of a right triangle that is always opposite the 90 degree angle

leg of a triangle

one of the two sides that form the right angle in a right triangle

parallelogram

a quadrilateral with two sets of opposite sides parallel and equal in length and congruent opposite angles

isometry

a transformation without a change to a figure's shape or size, such as rotation or reflection