Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 13
Math
Unit 6
7th Grade
Lesson 13 of 21
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Determine if three side lengths will create a unique triangle or no triangle.
The core standards covered in this lesson
7.G.A.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.
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
Using AngLegs or wooden skewers, investigate different side lengths that will create a triangle.
Complete the chart below, adding rows as needed.
What conclusion can you make about the side lengths of a triangle?
In each diagram below, line segment $${AB}$$ is 4 units. Two circles are drawn with a given radius and center at point $$A$$ and point $$B$$.
Diagram 1:
Circle with center $$A$$ has a radius of 4 units.
Circle with center $$B$$ has a radius of 2 units.
Diagram 2:
Circle with center $$A$$ has a radius of 1 unit.
a. Using Diagram 1, explain or show why you can create a triangle with side lengths 4 units, 4 units, and 2 units.
b. Using Diagram 2, explain or show why you cannot create a triangle with side lengths 4 units, 1 unit, and 2 units.
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
Which of the following set of side lengths could not be used to create a triangle?
A triangle has two side lengths that measure 6 in. and 9 in. Which of the following could be the measure of the third side? Select all that apply.
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 12
Lesson 14
Topic A: Angle Relationships
Identify and determine values of angles in complementary and supplementary 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
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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