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3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 1 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true Lesson Activity Investigating the 30°-60°-90° Triangle This activity will help you meet this educational goal: You will investigate the triangle and the extended ratio of its side lengths to solve for missing lengths in geometric figures. 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 In this activity, you will investigate the basis for the extended ratio of the triangle. To investigate the ratio, we will use an equilateral triangle with a side length of 2. Proceed to part A to begin. Part A On triangle , draw the altitude from vertex A to side . (Recall that an altitude is perpendicular to the line to which it is drawn.) Use the text box tool to label the point where the altitude meets side as point D. Then, determine the measures of and , and the length of . Using the text box tool, label the drawing with Question

3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 2 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true these measures. Submitted. Explanation:

3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 3 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true An altitude is perpendicular to the line to which it is drawn, thus forming a right angle. So is . Since the angle measures in a triangle sum to , is . Triangles and are congruent by the HL theorem since and is congruent to itself by the reflexive property. By CPCTC then, . For the two sides to be congruent and their sum to be 2 (since ), they both must have a length of 1. So

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3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 4 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true Part B Tiles Sequence Note that triangle from part A is a triangle. Drag the tiles to the correct box to show how the Pythagorean theorem can be used to find . Correct! Explanation: Question

3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 5 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true

3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 6 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true Part C Which extended ratio represents the relationship between the side lengths of triangle from the previous parts? Select the correct answer. Explanation: From part A, we know that and . From part B, the Pythagorean theorem revealed the length of . This information establishes the extended ratio of the side lengths for triangle as . Question

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3/12/24, 11 : 29 PM Lesson Activity: Investigating the 30°-60°-90° Triangle Page 7 of 7 https://app.edmentum.com/content-delivery/lessonactivity/7f36d5db-a1e8-428d-ba08-d41dd76131c5/ ? bucketType=2&includeExplain=true 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. Answer: 4 i feklt really good doing all of my notes Space used (includes formatting): 56 / 15000