G-CO.3.10

Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

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Formative Assessments
Formative Assessments
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Students are asked to prove the Triangle Inequality Theorem.
Proving the Triangle Inequality Theorem
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Students are asked prove that the measures of the interior angles of a triangle sum to 180°.
Triangle Sum Proof
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Students are asked to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side of the triangle and half of its length.
Triangle Midsegment Proof
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Assessment Questions
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Math Literature
Math Literature
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This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
Seven Circles I
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The goal of this task is to use similarity transformations to relate two triangles. The triangles in question are obtained by taking midpoints of two sides of a given triangle.
Midpoints of Triangle Sides
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The goal of this task is to help students synthesize their knowledge of triangles. They will need to know that a triangle inscribed in a circle, with a diameter of the circle as one side, is a right triangle.
Classifying Triangles
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The goal of this task is to establish that base angles in an isosceles triangle are congruent. There are many approaches to the task, several of which are presented here.
Congruent Angles in Isosceles Triangles
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This tasks examines how to calculate the area of an equilateral triangle using high school geometry, further developing ''8.G Areas of geometric shapes with the same perimeter'' which performs the same calculation at a level appropriate for middle school.
Finding the Area of an Equilateral Triangle
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The goal of this task is to provide an argument, appropriate for high school students, for why the sum of the angles in a triangle is 180 degrees.
Sum of Angles in a Triangle