Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 1
Math
Unit 6
7th Grade
Lesson 1 of 21
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Identify and determine values of angles in complementary and supplementary relationships.
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.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
Suggestions for teachers to help them teach this lesson
Students studied angles in fourth grade, where they recognized angles as shapes formed when two rays share a common endpoint. They understood that angle measures are additive, and they solved addition and subtraction problems to find missing angles. In this lesson, students formally define complementary and supplementary angles, and they start to develop their understanding of angle relationships and how they can represent these relationships using equations.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Use the diagram below to answer the questions.
a. Name an acute angle.
b. Name an obtuse angle.
c. Name a right angle.
d. Name two adjacent angles.
e. Name two nonadjacent angles.
Two angle diagrams are shown below. Use the information about each diagram to find the measure of the angle described.
a. Points $$Q$$, $$R$$, and $$T$$ lie on a straight line, as shown below. Find the measure of $$\angle SRT$$.
b. Angle $${ABC}$$ is a right angle. Find the value of $$x$$.
In the diagram below, point $$P$$ lies on line $${QT}$$.
a. Write and solve an equation to find the measure of $$x$$.
b. What is the measure of $$\angle RPT$$?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
In the diagram below, point $$A$$ lies on line $${BD}$$ and $$\angle CAE$$ is a right angle.
a. Describe the relationship between $$\angle DAE$$ and $$\angle EAB$$.
b. Name two angles that are complementary.
c. If the measure of angle $$DAC$$ is 74°, what is the measure of angle $$ DAE$$?
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.
Lesson 2
Topic A: Angle Relationships
7.G.B.5
Use vertical, complementary, and supplementary angle relationships to find missing angles.
Use equations to solve for unknown angles. (Part 1)
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.4 7.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.2 7.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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