Unit 5: Two-Dimensional Geometry
Summary/Overview:
Unit 5, Two-Dimensional Geometry addresses ideas about the attributes of 2-dimensional (2D) shapes, and how these attributes help students classify shapes. Students examine parallel and perpendicular lines, angles of 2D shapes with a special focus on quadrilaterals. Students learn to use a variety of tools and other methods to measure angles and explore the concept of rotation.
Objectives: Students will:
What Students Should Know:
- Two rays that meet at a common endpoint form an angle. A triangle is a polygon with three sides and three angles. A right triangle has one right angle. A right angle measures exactly 90 degrees. An obtuse triangle has one obtuse angle. An obtuse angle measures greater than 90 degrees. An acute triangle has all acute angles. An acute angle measures less than 90 degrees.
- Parallel and perpendicular lines are found in some geometric figures A line is a series of points that extend in two opposite directions without end. Perpendicular lines intersect to form four right angles. Parallel lines are lines in the same plane that never intersect.
- A quadrilateral is a polygon with four sides and four angles. A square is a polygon with four equal sides and four right angles. A parallelogram is a quadrilateral with opposite sides parallel and congruent. A rectangle is polygon with four sides and four right angles. A trapezoid is a quadrilateral with only one pair of parallel sides. A rhombus is a parallelogram with all four sides equal in length. Rhombi is more than one rhombus.
- quadrilateral is a polygon with four sides and four angles. A parallelogram is a quadrilateral with opposite sides parallel and congruent. A rectangle is polygon with four sides and four right angles. A rhombus is a parallelogram with all four sides equal in length. A square is a rectangle with four equal sides. A trapezoid is a quadrilateral with only four pair of parallel sides.
-Angles are formed by two rays that have the same endpoint/vertex. A protractor is a device used for measuring angles and creating angles. The steps to using a protractor are as follows: 1. place the point of the protractor on the vertex of the angle, 2. make sure that one side of the angle passes through zero on the scale. Start measuring from zero, 3. read the scale where it intersects the second side of the angle. An angle ruler is a clear plastic ruler that measures inches, centimeters, and degrees. Clear markings let students accurately construct and measure angles, triangles and other geometric shapes. Degrees are units to measure angles.
- A rotation turns a figure about a point. A half rotation is 180. A full rotation is 360.
What Students Should Be Able To Do:
Identify angles as acute, obtuse, and right Classify triangles based on their angles Find similarities and differences amongst the triangles and their angles
Identify parallel and perpendicular lines in a plane figure Describe the characteristics of parallel and perpendicular lines Find similarities and differences of parallel and perpendicular lines
Classify quadrilaterals as parallelograms, squares, rectangles, trapezoids, and rhombi Construct parallelograms, squares, rectangles, trapezoids, and rhombi
Compare and contrast parallelograms, squares, rectangles, trapezoids, rhombi
Accurately measure angles with the protractor or angle ruler Recognize that drawing a diagonal in a square will create two right angles Accurately fold strip of paper to specified degrees
Define half rotation/180 Define full rotation/360 Create a half rotation/180 Create a full rotation /360