Geometry Unit 2

Parallel lines-

Never meet and are always the same distance apart.

Obtuse angles-

Obtuse angles are *greater* than 90° and less than 180°

^Prisms-

Pizza boxes are rectangular prisms. a solid with two parallel congruent bases. think of these *bases* as the top and bottom of the box. The other four sides of the box are called *faces*. All prisms are made up of two parallel bases that are polygons, and faces that are parallelograms. The edges of the box are the *intersections* of the faces and bases. The corners of the box are called *vertices*.

Collinear points-

Points that lie on the same line.

*(Lesson 7) How to find the midpoint-

The midpoint of a line segment divides the line segment into two congruent segments.

Obtuse

are angles that measures greater than 90° but less than 180°.

Perpendicular lines (2)-

are two lines that intersect to form right angles.

Arcs

are used to show that angles have the same measurement on a diagram.

Perpendicular lines-

lines form a right angle

Intersecting lines-

lines meet at a point.

Right angles

measure 90°

How to find the length and midpoint of coordinate segments-

pp. 50-53 in Geometry.

The common endpoint of two rays

that make an angle is called the vertex.

Midpoint- (p. 23)

the midpoint of a segment is a point that divides the segments into two congruent segments.

Congruent angles have

the same measure

Opposite rays-

two rays that share the same endpoint and form a line.

(Absolute value lines) | ...| symbol turn-

|-12| into 12 Absolute value can never be negative.

If S is -4 and T is 8 what is the distance between them?

|-4 (-) 8| |-12| 12 units

Expressions: How to solve for x-

- Combine like terms. -Isolate the variable: Add or subtract the same value from both sides and then multiply or divide the same value from both sides.

Adjacent angles-

Are two angles that *share a vertex and a side* but open in different directions.

Angle bisector-

A ray that divides an angles into two congruent angles. You can define the angle bisector for an angle as a ray that creates two congruent angles.

Acute angles-

Acute angles are *less* than 90°

Fencing a Yard-

All is building a fence for a rectangular playground. She needs to know how many feet of fencing to buy- Perimeter, perimeter is the distance around a two-dimensional shape.

Angle-

An angle is formed by two rays with the same endpoint. The endpoint is the *vertex* of the angle.

Perpendicular bisector-

a line, segment, or ray that is perpendicular to the segment at its midpoint.

Three-dimensional shapes-

Cubes, spheres, and pyramids.

^Cones-

Ice cream cones are in the shape of a cone. a solid with one circular base and one vertex. You can think of the opening of the ice cream cone as the base and the bottom point of the cone as the vertex.

*Reading a protractor:*

If the angle opens from the right side then use the bottom of the scale. If the angle opens from the left side then use the top of the scale.

*(Lesson 6 pp. 43-45)* Tools for Geometry Constructions

Something with a straight edge. There are many geometric figures you can make with just a compass and a straightedge. Some objects, like the spinner and the calculator, can be traced to make an outline of that specific shape. But they won't help you create other shapes.

Two-dimensional shapes-

Squares, circles, and triangles.

^Pyramids-

The Great Pyramids of Egypt are pyramids. a solid with one base that is shaped like a polygon. Pyramids found in Egypt all have square or rectangular bases. The faces of a pyramid are always triangles.

------------------------------------------------

-----------------------------------------

Straight angles measure

180°

How many methods are used for naming angles?

3 methods.

A circle measures

360°

*(Lesson 3pp. 20-23)* Measuring on a Number Line: What is the distance between -2 and 3?

5. The number of -2 is 5 units away from the number 3. Because the distance is positive, find the distance between the two points: | -2 (-) 3| = 5

Bisectors-

A bisector of a line segment divides the segment into two congruent segments, so the segments should have the same measure.

^Cylinders-

A can of soup is in a shape of a cylinder. Like the prism, it has two parallel, congruent bases. The difference is that the bases of a cylinder are circles.

Skew lines-

A line on a highway and a line on an overpass are examples of skew lines. These are lines that are neither parallel nor intersecting because they lie in different planes.

Plane-

A plane is represented by a flat surface (like a square) that extends without end and has no thickness. A plane contains infinitely many lines. The symbol used to represent a plane is a slanted four-sided figure, called a parallelogram. is represented by a flat surface that extends without end and has no thickness. A plane contains infinitely many lines. How to name it: You can name a plane by a capital letter, such as plane "P" or by at least three points in the plane that do not all lie on the same line.

^Spheres-

A soccer ball is a sphere. a solid with all points the same distance from a given point called the *center*.

[Naming solid figures]-

A solid is a three-dimensional figure that has length, width, and depth, and encloses part of a space.

*(Lesson 2 pp. 11-15)* (See notebook for examples) Point-

Indicates location. A point has no dimensions, meaning it has no length, no width, and no height. Points are used to determine planes, lines, rays, and segments. A point indicates a location and has no size. The symbol used to represent a point is a dot like the one seen below. A point is named using a capital letter. Indicates a location and has no size. How to name it: You can represent a point by a dot and same it by a capital letter such as "A."

Coplanar-

Points and lines that lie on the same plane. All points of a line are coplanar.

Labeling an Ordered Pair (coordinates)-

Positive x-coordinates- Right side Negative x-coordinates- Left side Positive y-coordinates- top Negative y-coordinates- bottom

Line-

Represents a straight path that extends in both directions. A line has no thickness and is represented by a straight path that extends in two opposite directions without end. A line contains infinitely many points. Is represented by a straight path that extends in two opposite directions without end and has no thickness. A like contains infinitely many points. How to name it: You can name a line by any two points on the line, such as AB or BA or a lower case l.

*(Lesson 4 pp. 27-30)* Right angles-

Right angles are 90°

*(Lesson 8)* Perimeter and Area of Rectangles-

The side lengths of the rectangles are measured in centimeters, so the perimeter and area will be written in centimeters. To find the perimeter, add the lengths of all sides. To find the area, multiply the length and width.

*(VOCAB DEFINITIONS)* Rays-

The sides of an angle.

Orthographic drawing- (bp. 6)

This type of drawing involves three separate views of the figure, such as the top view, front view, and right-side view. Solid lines are used to show visible edges while dashed lines are used to show hidden edges.

Isometric drawing- (bp 5)

This type of drawing shows a CORNER view that allows you to see the top, front, and side of the figure. Slanted lines are used to represent the depth of the three-dimensional figure.

Supplementary angles/Linear pair-

Two angles whose measures add up to 180 degrees, forming a straight angle.

Complementary angles-

Two angles whose measures add up to 90 degrees. 30 degrees + 60 degrees = 90 degrees

Vertical angles-

Two lines that intersect to form two pairs of opposite angles. Vertical angles are ALWAYS congruent, meaning there measure is always the same.

Congruent segments-

Two segments that have the same length. (p. 22)

Naming line segments:

You can name a segment using it's two end points and the line segment symbol. If one end is A and the other is C it can be named AC or CA.

*(Lesson 5 pp. 34-37)* Naming Angles-

You can name an angle by its vertex, a number, or a point on a ray, followed by its vertex, followed by a point on the other ray

_______________________________________________________

____________________________________________________

Ray-

a part of a line that is bounded at one end by a point and extends indefinitely in the other direction. A ray is part of a line that consists of one endpoint and all the points of the line on one side of the end point.

Protractor-

a tool used to measure angles.

Angles are measured in units of

degrees.

Net- (bp. 4)

is a two-dimensional diagram that can be folded to form a three-dimensional figure. (An unfolded representation of a shape like a cube or pyramid)

Acute angles

measure less than 90°

Line segment-

part of a line that is bounded by two endpoints. Segments are parts of lines that are bound by two fixed endpoints. part of a line that consists of two endpoints and all points between them.

The real number that corresponds to a point-

the coordinate of the point.

When using 3 letters to name an angle, the middle letter represents the

vertex.