Lesson 1 Proportions in Right Triangles (Geometric Mean Proportions)
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How did you prepare/study for the exam? If you were to take this exam again is there anything you would do differently to prepare for the exam?
Which topic on the exam did you feel most prepared for /comfortable with?
Which topic on the exam do you feel like you struggled most with / need more time to review/understand/master?
Up on boards your group must share at least one of your discussion points.
Lesson 1 Proportions in Right Triangles (Geometric Mean Proportions)
Be able to identify the similar triangles formed by the altitude drawn to the hypotenuse.
Be able to derive the geometric mean formulas by writing proportions involving side ratios of the similar triangles
Be able to find missing legs/hypotenuses/altitude/hypotenuse segments by writing and solving proportions derived from the corresponding sides of similar triangles.
Be able to calculate the geometric mean between two numbers
To find the Geometric Mean of two numbers you can use the cross products property of proportions
***Note: You will have to be able to simplify radicals to find geoemtric means. If you need a review please see this link to a Formative exercise that reviews Simplifying Radicals
Find the geometric mean between 2 and 32.
Find the geometric mean between 4 and 25.
Let's summarize how to find a geometric mean. To find the geometric mean between two numbers simply
Step 1:
Step 2:
What similarity statement can you write relating the three triangles in the diagram?
By using the cross products property, you can derive the following formula:(Use the similar Triangle Method)
(Use Geometric Mean Proportion Method)
By using the cross products property, you can derive the following formula:
(Use similar Triangle Method)
(Use Geometric Mean Proportion Method)
What is the geometric mean of 4 and 9?
What is the geometric mean of 4 and 12? Write in simplest radical form.
Create a Cheat Sheet for Today's Lesson. Summarize the key points (Include important terms and theorems) from today's lesson. Your cheat sheet should include an example problem(s)
Which statement is always TRUE?
Which equation is always TRUE?
Which statement must always be TRUE?
In simplest radical form
Identify the parts of
Hypotenuse:
"Short" Leg :
"Long" Leg:
Altitude:
What is the relationship between the three triangles?
In a very informal proof, how can you prove the relationship between the triangles you found in the previous question.
In your own words, starting with ONE right triangle how do you form 2 triangles that are similar to the original triangle (write no more than 2 lines of text --> keep brief)
Where do you think we are going with this? What will be able to do (solve for/find) when given the altitude drawn to the hypotenuse?
Which of the following are true? (select all that apply.)
Why are all three statements (proportions) in the previous question TRUE? (be brief --> no more than 2 lines of text)
How are these similar triangle proportions a little different / a little special from previous similar triangles we have looked at (like the two warmup problems from the start of class).
Find the geometric mean between 8 and 10. Write your answer in simplest radical form.
Find the geometric mean between 3 and 9. Write your answer in simplest radical form.
From the similarity statement you found in the previous question, which ratio equals
? (Select all that apply.)