In this unit students will:
• draw geometric figures using rulers and protractor with emphasis on triangles
• write and solve equations involving angle relationships
• explore two-dimensional cross-sections of cylinders, cones, pyramids, and prisms
• know and use the formula for the circumference and area of a circle
• solve engaging problems that require determining the area, volume, and surface area of
fundamental solid figures.

Vocabulary

• Adjacent Angle: Angles in the same plane that have a common vertex and a common side, but no common interior points.

• Circumference: The distance around a circle.

• Complementary Angle: Two angles whose sum is 90 degrees.

• Congruent: Having the same size, shape and measure. ∠A ≅∠ B denotes that ∠A is congruent to ∠B.

• Cross- section: A plane figure obtained by slicing a solid with a plane.

• Irregular Polygon: A polygon with sides not equal and/or angles not equal.

• Parallel Lines: Two lines are parallel if they lie in the same plane and they do not intersect. AB

CD denotes that AB is parallel to CD .

• Pi: The relationship of the circle’s circumference to its diameter, when used in calculations, pi is typically approximated as 3.14; the relationship between the circumference (C) and diameter (d), 𝐶 ≈ 3 1/7 or 3.14 or 22/7

• Regular Polygon: A polygon with all sides equal (equilateral) and all angles equal (equiangular).

• Supplementary Angle: Two angles whose sum is 180 degrees.

• Vertical Angles: Two nonadjacent angles formed by intersecting lines or segments. Also called opposite angles.

7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Video: Draw geometric shapes given the length of sides Video:Draw triangles using given angles Video: Determine if given measurements will allow you to create the appropriate shape Video: Draw a polygon using more than one condition

7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Video: Describe 2-dimensional cross sections of right rectangular prisms Video: Describe 2-dimensional cross sections of right rectangular pyramids

7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Video: Determine the measures of a circle Video: Find the circumference of a circle Video: Find the area of a circle Video: Use circumference to solve for area Video: Use area of a circle to solve for circumference

7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Video:Find angle measurements using complementary and supplementary angles Video: Write and solve equations using complementary and supplementary angles Video: Find angle measurements using vertical angles Video: Write equations using vertical angles Video: Write equations for problems using facts about angle relationships

7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Video:Find surface area of cubes and prisms by pulling them apart Video: Find surface area of cubes of prisms using formulas Video: Find missing dimensions using the volume formula Video: Choose the appropriate measurement for solving a problem

Chapter 1: Foundations of GeometryChapter 2: Geometric ReasoningChapter 3: Parallel and Perpendicular LinesChapter 4: Triangle CongruenceChapter 5: Properties and Attributes of TrianglesChapter 6: Polygons and QuadrilateralsChapter 7: SimilarityChapter 8: Right Triangles and TrigonometryChapter 9: Extending Perimeter, Circumference, and AreaChapter 10: Spatial ReasoningChapter 11: CirclesChapter 12: Extending Transformations Geometry## Overview

In this unit students will:• draw geometric figures using rulers and protractor with emphasis on triangles

• write and solve equations involving angle relationships

• explore two-dimensional cross-sections of cylinders, cones, pyramids, and prisms

• know and use the formula for the circumference and area of a circle

• solve engaging problems that require determining the area, volume, and surface area of

fundamental solid figures.

## Vocabulary

•Adjacent Angle:Angles in the same plane that have a common vertex and a common side, but no common interior points.•

Circumference:The distance around a circle.•

Complementary Angle:Two angles whose sum is 90 degrees.•

Congruent:Having the same size, shape and measure. ∠A≅∠Bdenotes that ∠Ais congruent to ∠B.•

Cross- section:A plane figure obtained by slicing a solid with a plane.•

Irregular Polygon:A polygon with sides not equal and/or angles not equal.•

Parallel Lines:Two lines are parallel if they lie in the same plane and they do not intersect.ABCDdenotes thatABis parallel toCD.•

Pi:The relationship of the circle’s circumference to its diameter, when used in calculations, pi is typically approximated as 3.14; the relationship between the circumference (C) and diameter (d), 𝐶 ≈ 3 1/7 or 3.14 or 22/7•

Regular Polygon:A polygon with all sides equal (equilateral) and all angles equal (equiangular).•

Supplementary Angle:Two angles whose sum is 180 degrees.•

Vertical Angles:Two nonadjacent angles formed by intersecting lines or segments. Also called opposite angles.7.G.2.Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.Video: Draw geometric shapes given the length of sides

Video: Draw triangles using given angles

Video: Determine if given measurements will allow you to create the appropriate shape

Video: Draw a polygon using more than one condition

7.G.3.Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.Video: Describe 2-dimensional cross sections of right rectangular prisms

Video: Describe 2-dimensional cross sections of right rectangular pyramids

7.G.4.Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.Video: Determine the measures of a circle

Video: Find the circumference of a circle

Video: Find the area of a circle

Video: Use circumference to solve for area

Video: Use area of a circle to solve for circumference

7.G.5.Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.Video: Find angle measurements using complementary and supplementary angles

Video: Write and solve equations using complementary and supplementary angles

Video: Find angle measurements using vertical angles

Video: Write equations using vertical angles

Video: Write equations for problems using facts about angle relationships

7.G.6.Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.Video: Find surface area of cubes and prisms by pulling them apart

Video: Find surface area of cubes of prisms using formulas

Video: Find missing dimensions using the volume formula

Video: Choose the appropriate measurement for solving a problem