Lesson 10
Drawing Triangles (Part 2)
Let’s draw some more triangles.
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.
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010149Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=38667982ef0cd06865556226f663e0b49b26d5b645887adfc9e67f7418588d68)
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.
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010149Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4343734d4da3ebf3b54d717285701b5b200cc3e99019a799c7dac16272aff992)
Problem 5
Match each equation to a step that will help solve the equation for \(x\).
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?