Geometry unit
MEASUREMENT AND GEOMETRY (7TH GRADE)
7.6 a) compare and contrast quadrilaterals based on their properties; b) determine unknown side lengths or angle measures of quadrilaterals.
MEASUREMENT AND GEOMETRY (6TH GRADE)
a) derive π (pi); b) solve problems, including practical problems, involving circumference and area of a circle; c) solve problems, including practical problems, involving area and perimeter of triangles and rectangles. 6.8 a) identify the components of the coordinate plane; b) identify the coordinates of a point and graph ordered pairs in a coordinate plane. 6.9 determine congruence of segments, angles, and polygons.
6.9 , 7.6 Congruence and Quadrilaterals
congruent - geometric figures that are the same size and same shape line of symmetry - If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. angle - the amount of turn between two lines around their common point (the vertex). line segment - the part of a line that connects two points vertex, vertices (plural) - a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices. degrees - a measure for angles. There are 360 degrees in a full rotation. The symbol for degrees is ° ray - a part of a line with a start point but no end point (it goes to infinity) closed figure - a shape where all line segments are connected open shape - an open shape is made up of line segments, but there is at least one line segment that isn't connected to anything at one of its endpoints. hatch (hash) marks - a symbol used on geometric figures to denote equality of length or tell if lines are parallel polygon - a closed plane shape (two-dimensional) with straight sides. regular polygon - A polygon is regular when all angles are equal and all sides are equal (otherwise it is irregular) plane - A flat surface with no thickness. It extends forever. We often draw a plane with edges, but it really has no edges. plane figure - flat two-dimensional shape. It can be made of both straight and curved lines. parallel - always the same distance apart and never touching. perpendicular - lines that cross and form right angles or line segments that would eventually cross at right angles if extended adjacent - next to each other diagonal - a line segment that goes from one corner to another, but is not an edge
6.8 Cartesian Coordinate System
coordinate plane - a two-dimensional number line system where the vertical line is called the y-axis and the horizontal is called the x-axis. ordered pair - a way to pinpoint where you are on a map or graph by how far along and how far up or down the point is. origin - the coordinate point (0,0) quadrants - four sections on a coordinate plane x-coordinate - the horizontal value in a pair of coordinates y-coordinate - the vertical value in a pair of coordinates
6.7 Circles
perimeter - Perimeter is the distance around a two-dimensional shape. area - The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle, rectangle, or circle. circumference - The distance around the edge of a circle (or any curvy shape). It's a type of perimeter. formula - usually written as an equation, using symbols to describe a certain relationship between quantities. It's used to find a missing value. diameter - The distance from one point on a circle through the center to another point on the circle. It is also the longest distance across the circle and it is twice the radius. radius - The distance from the center to the circumference of a circle. Divide the diameter by two to find the radius. pi - The ratio of a circle's circumference to its diameter. In other words: all the way around a circle divided by all the way across it. The symbol is π and approximately 3.14. No matter how large or small the circle, its circumference is always π times its diameter. derive pi - any activity that demonstrates the ratio of the circumference of any circle to its diameter, regardless of the circle's size, will always equal pi. For example, we used string, four different sized circles, and a cookie to show this relationship.
Quadrilaterals
quadrilateral - a flat closed shape exactly four straight sides. trapezoid - a flat closed shape with 4 straight sides that has a pair of opposite sides parallel. (United States Definition) trapezium - a flat closed shape with 4 straight sides NONE of which are parallel. (United States Definition) isosceles trapezoid - the base angles are equal and therefore the left and right side lengths are also equal. right trapezoid - a trapezoid with has two adjacent right angles parallelogram - A flat shape with 4 straight sides where opposite sides are parallel and congruent. Also opposite angels are congruent. kite - each pair of adjacent sides that are congruent. Also one pair of opposite angles are congruent. rectangle - a four sided flat shape with straight sides where all interior angles are right angles (90°). Also opposite sides are parallel and of equal length. rhombus - a flat shape with four straight sides that are all equal length. Also opposite sides are parallel and opposite angles are equal. square - a flat shape with four straight sides where all sides have equal length, and every interior angle is a right angle (90°)