Lesson 10
Drawing Triangles (Part 2)
Problem 1
A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many unique triangles can be drawn that fit that description? Explain or show your reasoning.
Solution
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Problem 2
A triangle has one side that is 5 units long and an adjacent angle that measures \(25^\circ\). The two other angles in the triangle measure \(90^\circ\) and \(65^\circ\). Complete the two diagrams to create two different triangles with these measurements.
![Two images, each a segment with side 5 and a dotted line rising at a 25 degree angle from the segment.](https://cms-im.s3.amazonaws.com/JCtfx5hUae7VFyxFFbC2YGVh?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP.twotriangles005.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP.twotriangles005.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5ea7b680d60250deaa319869ca5a6d036e4c07617fb53bbf962aa2c69563535d)
Solution
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Problem 3
Is it possible to make a triangle that has angles measuring 90 degrees, 30 degrees, and 100 degrees? If so, draw an example. If not, explain your reasoning.
Solution
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Problem 4
Segments \(CD\), \(AB\), and \(FG\) intersect at point \(E\). Angle \(FEC\) is a right angle. Identify any pairs of angles that are complementary.
![Segment C D, segment A, B, segment F G intersect at point E. Clockwise, the points are C, F, B, D, G, A. Angle F E C is a right angle.](https://cms-im.s3.amazonaws.com/KEznEkCJSRVkeUvcBU1GjPUq?response-content-disposition=inline%3B%20filename%3D%227-7.7.A2.new.PP.0001abc.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.A2.new.PP.0001abc.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4011527a50d6978af92ff2c0e227fc749ee31b7f6a181a7ac89f39e43b195760)
Solution
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(From Unit 7, Lesson 2.)Problem 5
Match each equation to a step that will help solve the equation for \(x\).
Solution
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(From Unit 5, Lesson 15.)Problem 6
- If you deposit $300 in an account with a 6% interest rate, how much will be in your account after 1 year?
- If you leave this money in the account, how much will be in your account after 2 years?
Solution
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(From Unit 4, Lesson 8.)