Inscribed Polygons_ Tutorial2.0

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University of South Carolina *

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A503

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Physics

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Apr 3, 2024

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3/14/24, 8:00 PM Lesson Activity: Constructing an Equilateral Triangle from a Diameter https://f2.app.edmentum.com/courseware-delivery/ua/134709/45616281/aHR0cHM6Ly9mMi5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmVy… 1/5 Lesson Activity Constructing an Equilateral Triangle from a Diameter This activity will help you meet this educational goal: You will recognize and justify a construction of an equilateral triangle. Directions Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work. Activity Given circle O, Holly drew diameter . She then used a compass to draw an arc centered at Q, passing through point O, and intersecting circle O at two points. She labeled the points of intersection R and S, as shown, and drew chords , , and . Holly claims triangle is equilateral.

3/14/24, 8:00 PM Lesson Activity: Constructing an Equilateral Triangle from a Diameter https://f2.app.edmentum.com/courseware-delivery/ua/134709/45616281/aHR0cHM6Ly9mMi5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmVy… 2/5 Part A Given the steps Holly used in her construction, complete the statement to make it true. Select the correct answer from each drop-down menu. The measure of arc is 30° 45° 60° 90° , and the measure of arc is 60° is 90° is 120° is 180° cannot be determined . Correct! Explanation: We saw in our earlier constructions that arcs drawn using a compass setting equal to the radius of a given circle will partition the circle into six congruent arcs, each with a measure of . Because arcs and were drawn with the compass set at the length of radius , we can determine and . Question

3/14/24, 8:00 PM Lesson Activity: Constructing an Equilateral Triangle from a Diameter https://f2.app.edmentum.com/courseware-delivery/ua/134709/45616281/aHR0cHM6Ly9mMi5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmVy… 3/5 Part B Select all the correct answers. Which three statements are true about Holly's construction? Correct! Explanation: We saw in part A that and . Because is a diameter, arcs and are each a semicircle with a measure of . We can subtract from to find . So, arcs , , and are all congruent. Question Arc is congruent to arc . Arc is a semicircle. Chord is congruent to chord . Arc is a semicircle. Arc is congruent to arc .

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3/14/24, 8:00 PM Lesson Activity: Constructing an Equilateral Triangle from a Diameter https://f2.app.edmentum.com/courseware-delivery/ua/134709/45616281/aHR0cHM6Ly9mMi5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmVy… 4/5 Part C How can the answers to parts A and B be used to show how Holly constructed an equilateral triangle? Answer: The answers to parts a and b can be used to determine if Holly constructed an equilateral triangle by checking if the triangle satisfies the properties of an equilateral triangle Space used (includes formatting): 983 / 15000 Because congruent arcs on a circle are intercepted by congruent chords, and we saw in part B that arcs , , and are all congruent, we can conclude that chords , , and are all congruent. So, the sides of are congruent, and is equilateral. Hide Sample Answer Self-Evaluation How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

3/14/24, 8:00 PM Lesson Activity: Constructing an Equilateral Triangle from a Diameter https://f2.app.edmentum.com/courseware-delivery/ua/134709/45616281/aHR0cHM6Ly9mMi5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmVy… 5/5 Answer: 5. I learned a lot about triangles and how they work. It challeneged me when it asked me to example it but i worked through it and i think i did very good. Space used (includes formatting): 162 / 15000

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