2D Geometry

Unit Review Sheet

Facts and Definitions

Lesson 1: Lines and Angles

• A plane is a flat surface that has no depth but extends forever in all directions.
• A point is a specific location on a plane.
• A line in geometry is a group of points that connect to make a straight line that extends forever in two opposite directions.
• A line segment is a section of a line; it has finite length and two endpoints.
• A ray is a section of a line that has one endpoint and extends forever in one direction.
• Intersecting lines meet or cross each other. Intersecting lines that form a 90° angle where they intersect are perpendicular.
• If two coplanar lines never meet — that is, they are always the same distance apart — they are parallel.
• A polygon is a closed 2D shape made up of at least three straight line segments.
• An angle is formed by the intersection of two lines, line segments, or rays.
• The sides of an angle are called its arms, and the point where the arms meet is the vertex.
• Acute angles measure less than 90°, right angles measure exactly 90°, obtuse angles measure greater than 90° but less than 180°, and straight angles measure exactly 180°.
• A reflex angle measures greater than 180° but less than 360°.
• A protractor is a tool used to measure angles.
• If the sum of the measures of two angles is exactly 90 degrees, the angles are complementary angles.
• Adjacent angles are angles that share a common arm and vertex.
• If the sum of the measures of two angles is exactly 180 degrees, the angles are supplementary angles.
• When two lines intersect, the angles opposite to each other are congruent and are called vertical angles.

Lesson 2: Working With Angles

• Variables can be used to represent unknown measures in geometry problems.
• Equations are solved using inverse operations to find the value of a variable.
• The value of a variable may be the value of the unknown measure, or it may be a part of an expression that represents the unknown measure.

Lesson 3: Triangles

• A triangle can be equilateral (all sides congruent), isosceles (two sides congruent), or scalene (no sides congruent).
• A triangle can be acute (all acute angles), right (one right angle), or obtuse (one obtuse angle).
• A triangle can have a binomial label based on both the sides and angles of the triangle.
• The measures of the three angles in a triangle always add up to 180°.
• The sum of the lengths of the two shorter sides of a triangle is always greater than the length of the longest side of the triangle.
• A triangle can be drawn using a protractor and ruler if you know the measure of at least three parts of the triangle.
• A unique triangle is one that cannot be drawn in more than one way given certain conditions.
• Corresponding parts of geometric figures are the parts (angles and sides) that are in the same position in relation to the other parts of the figure.
• Congruent figures are geometric figures that are identical in all their corresponding parts.
• Similar figures are geometric figures that have the same shape but not the same size.

Lesson 4: Area

• Area is the measure of space inside a two-dimensional shape.
• The base of a 2-D geometric figure is the bottom line of the figure.
• The height of a 2-D geometric figure is the vertical distance from the base to an opposite side or point.
• The area of a parallelogram is found by multiplying the base times the height. (A = b × h)
• The area of a triangle is found by multiplying 1/2 times the base times the height. (A = 1/2 × b × h)
• Complex polygons can be decomposed into simpler shapes to make finding the area less complicated.

Lesson 5: Circles

• Circle: a two-dimensional figure made of a set of points that are all the exact same distance from a single point.
• Center: the point inside a circle that is an equal distance from all points on the circle.
• Radius: the distance from the center point to any point on the circle.
• Diameter: the line segment that passes through the center point and connects two points on the circle.
• The diameter of a circle is twice as long as the radius. The radius of a circle is half as long as the diameter.
• Circumference: the measure of distance around the outside of the circle.
• Pi (π) is the relationship of a circle's circumference to its diameter. It is an irrational number. The value 3.14 is used for basic computation needs.
• Two formulas can be used to find the circumference of a circle: C = πd or C = 2πr.
• The formula for the area of a circle is A = πr².

Lesson 6: Scale Drawings

• A scale drawing shows an object that has been enlarged or reduced from its real size using a set scale factor.
• A scale drawing can represent an enlargement or reduction in size.
• Similar figures have the same shape but are different sizes.
• The scale factor defines the relationship between the linear measures of the original figure and the corresponding linear measures of the scale drawing. It can be shown as a ratio or a percentage.
• The perimeter of a scale drawing is changed by the same ratio as the scale factor. The area of a scale drawing is changed by the ratio that is the square of the scale factor.

Lesson 7: Unit 6 Test

• [none]

Final Project: Geometry Stations

• [none]