Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 2
Math
Unit 6
7th Grade
Lesson 2 of 21
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Lesson Notes
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Use vertical, complementary, and supplementary angle relationships to find missing angles.
The core standards covered in this lesson
7.G.B.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.
The foundational standards covered in this lesson
4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.C.7 — Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
In small groups, with a ruler, draw two intersecting lines on a piece of paper.
Vertical angles are a pair of angles formed across from one another when two lines intersect. Based on the data from your class, what can you conclude about the measurements of vertical angles?
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In the diagram below, line $${CD}$$ intersects line $${AB}$$ through point $$E$$. Ray $$EF$$ extends from point $$E$$.
Callie says that $$\angle CEB$$ is vertical to $$\angle AEF$$. Explain why her reasoning is incorrect and name the angle that is vertical to $$\angle CEB$$.
Three lines meet at a point, as shown below.
a. Describe the angle relationships you see in the diagram.
b. Set up and solve an equation to find the value of $$z$$.
Grade 7 Mathematics > Module 6 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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15-20 minutes
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5-10 minutes
Three lines intersect at a common point, as shown in the diagram below.
Write and solve an equation to determine the value of $$x$$.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Use equations to solve for unknown angles. (Part 1)
Topic A: Angle Relationships
Identify and determine values of angles in complementary and supplementary relationships.
Standards
7.G.B.5
Use equations to solve for unknown angles. (Part 2)
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Topic B: Circles
Define circle and identify the measurements radius, diameter, and circumference.
7.G.B.4
Determine the relationship between the circumference and diameter of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.
Determine the relationship between the area and radius of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.
Solve problems involving area and circumference of two-dimensional figures (Part 1).
7.G.B.47.G.B.6
Solve problems involving area and circumference of two-dimensional figures (Part 2).
Topic C: Building Polygons and Triangles
Draw two-dimensional geometric shapes using rulers, protractors, and compasses.
7.G.A.27.G.B.5
Determine if three side lengths will create a unique triangle or no triangle.
7.G.A.2
Identify unique and identical triangles.
Determine if conditions describe a unique triangle, no triangle, or more than one triangle.
Topic D: Solid Figures
Identify and describe two-dimensional figures that result from slicing three-dimensional figures.
7.G.A.3
Find the surface area of right prisms.
7.G.B.6
Find the surface area of right pyramids.
Find the volume of right prisms and pyramids.
Solve real-world and mathematical problems involving volume.
Distinguish between and solve real-world problems involving volume and surface area.
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