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Circles and Segments

Resource:
Circles and Segments

These four parts are designed to support students in making connections between chord, secant, and tangent line relationships in circles and creating proofs of these relationships using triangle similarity.

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• Unit 7

#### Circles

Circles and Squares

Resource:
Circles and Squares

In this task, you must solve a problem about circles inscribed in squares.

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• Unit 7

#### Circles

Right Triangles Inscribed in Circles 1

Resource:
Right Triangles Inscribed in Circles 1

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

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• Unit 7

#### Circles

Right Triangles Inscribed in Circles 2

Resource:
Right Triangles Inscribed in Circles 2

The result here complements the fact, presented in the task ''Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.

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• Unit 7