MIDTERM :(

Question 1

Define endpoint

Answer 1

The point located at the very end of a line segment (or the definite end of a ray)

Question 2

Define bisector

Answer 2

A point, line, segment, ray, or plane that cuts a line, segment, ray, angle, or plane in half

Question 3

Define midpoint

Answer 3

A point that divides a segment into two congruent segments

Question 4

Define congruent

Answer 4

Equal to/of the same measure (may be same length, distance, degrees, etc.)

Question 5

Define complementary angles

Answer 5

Angles that add up to 90

Question 6

Define supplementary angles

Answer 6

Angles that add up to 180

Question 7

Define vertical angles

Answer 7

Angles that are opposite each other, share a vertex, form opposite rays, and are congruent

Question 8

Define parallel lines

Answer 8

Lines on the same plane that have the same slope and never intersect

Question 9

Define perpendicular lines

Answer 9

Lines that intersect to form a 90 degree angle

Question 10

Define transversal

Answer 10

A line that cuts through a pair of parallel lines

Question 11

Define transformation

Answer 11

A change to the location, size, or orientation of a given shape

Question 12

Define rigid transformation

Answer 12

A transformation in which the image and pre-image are congruent, with angles and sides of the same measure

Question 13

Define non-rigid transformation. Give an example

Answer 13

A transformation in which the size and/or structure of the pre-image is changed

E.g. dilations, in which the pre-image and image are similar, the corresponding angles are congruent, but the corresponding sides are proportional

Question 14

Define pre-image

Answer 14

A shape shown before a transformation is applied to it

Question 15

Define image

Answer 15

A shape after a transformation has been applied to it

Question 16

Define translation

Answer 16

A rigid transformation in which each point of a figure moves the same distance and in the same direction, making the image and pre-image congruent

Question 17

Define reflection

Answer 17

A rigid transformation in which a figure is reflected/flipped over a line, making the image and pre-image congruent

Question 18

Define rotation

Answer 18

A rigid transformation (pre-image and image are congruent) in which a figure is turned (or rotated) around a fixed point through a given angle (measurement)

Question 19

What does rotating something clockwise mean? Counterclockwise?

Answer 19

The image is turned around the point to the right
The image is turned around the point to the left

Question 20

Define dilation

Answer 20

A non-rigid transformation (pre-image and image are similar, with congruent corresponding angles and proportional corresponding sides) in which each point of a figure stretches or shrinks with respect to a fixed point

Question 21

Define triangle sum theorem

Answer 21

All interior angles in a triangle add up to 180, and exterior angles add to 360

Question 22

Define exterior angle theorem

Answer 22

The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

Question 23

How do you name a point? Example.

Answer 23

Point ___(capital letter)____
E.g. point A

Question 24

How do you name a point? Example.

Answer 24

Point ___(capital letter)____
E.g. point A

Question 25

How do you name a plane? Example.

Answer 25

Plane __(three co-planer points)__ OR plane __(capital letter)__ E.g. plane ABC or plane H

Question 26

How do you name a ray? Example.

Answer 26

Ray __(endpoint and another point on the ray)__ E.g. ray AB

Question 27

How do you name a line segment? Example

Answer 27

Line segment __(both endpoints)__ E.g. line segment XY

Question 28

How do you name an intersection of two lines? Example

Answer 28

Point __(point of intersection)__ E.g. (x) the middle of this "x" is point D

Question 29

How do you name an intersection of a line and a plane? Example

Answer 29

Point __(point of intersection)__ E.g. point G

Question 30

How do you name an intersection of two planes? Example

Answer 30

Line __(line of intersection)__ E.g. line F

Question 31

What do you use the segment addition postulate for? How? Example

Answer 31

Finding the length of a line segment that is composed of two smaller connected segments Add the two segment lengths together E.g. (A---B---C) AB+BC=AC

Question 32

What do you use the angle addition postulate for? How? Example

Answer 32

Finding the measure of an angle that is composed of two smaller angles (or find the measure of one of the smaller angles if given the other small angle measurement and the full measure) Add the angles' measures together E.g. ( \/_ ) ∠ABC + ∠BCD = ∠ABD

Question 33

How do you find an endpoint when you are given a midpoint (1,4) and another endpoint (3,6)?

Answer 33

Use the midpoint formula: (x1+x2 / 2, y1+y2 / 2) Plug the midpoint coordinates in so it reads: (1=x1+x2 /2, 4=y1+y2 /2) Plug in the endpoint coordinates for x1 and y1: (1=3+x /2, 4=6+y /2) Solve: [1*2=2(3+x/2), 4*2=2(6+y/2)] [2=3+x, 8=6+y] [2-3=3-3+x, 8-6=6-6+y] [-1=x, 2=y] Endpoint = (-1, 2)