Test 2.1 - Proportionality and Similar Triangles Debrief

You have 5 minutes to discuss the following:

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.

Review of Finding Side lengths of Similar Triangles

1

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

On the next slide play around with the animation before answering questions on the following slide

1

Geometric Mean

null To find the Geometric Mean of two numbers you can use the cross products property of proportions

Cross Multiply

null

***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

1

What similarity statement can you write relating the three triangles in the diagram?

1

null

The ALTITUDE is the Geometric Mean between the two hypotenuse segments.

By using the cross products property, you can derive the following formula:

Altitude² = Segment of hypotenuse₁ x Segment of hypotenuse₂

1

The LEG is the Geometric mean between the HYPOTENUSE and the ADJACENT hypotenuse segment

null By using the cross products property, you can derive the following formula:

Leg² = Hypotenuse x Segment of hypotenuse adjacent to leg

1

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?

1

Which equation is always TRUE?

1

Which statement must always be TRUE?

1

Lesson 1 Proportions in Right Triangles (Geometric Mean Proportions)

Review of Finding Side lengths of Similar Triangles

More Problems _-> Complete in your Groups - use whichever method you are most comfortable with.

More problems (reps)

Lesson 1 Proportions in Right Triangles (Geometric Mean Proportions)

Test 2.1 - Proportionality and Similar Triangles Debrief

You have 5 minutes to discuss the following:

Review of Finding Side lengths of Similar Triangles

On the next slide play around with the animation before answering questions on the following slide

Geometric Mean

What similarity statement can you write relating the three triangles in the diagram?

The ALTITUDE is the Geometric Mean between the two hypotenuse segments.

By using the cross products property, you can derive the following formula:

Altitude2 = Segment of hypotenuse1 x Segment of hypotenuse2

The LEG is the Geometric mean between the HYPOTENUSE and the ADJACENT hypotenuse segment

Leg2 = Hypotenuse x Segment of hypotenuse adjacent to leg

More Problems _-> Complete in your Groups - use whichever method you are most comfortable with.

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)

More problems (reps)

Which statement is always TRUE?

Which equation is always TRUE?

Which statement must always be TRUE?

Test 2.1 - Proportionality and Similar Triangles Debrief

You have 5 minutes to discuss the following:

On the next slide play around with the animation before answering questions on the following slide

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).

Geometric Mean

What similarity statement can you write relating the three triangles in the diagram?

From the similarity statement you found in the previous question, which ratio equals ? (Select all that apply.)

The ALTITUDE is the Geometric Mean between the two hypotenuse segments.

By using the cross products property, you can derive the following formula:

Altitude2 = Segment of hypotenuse1 x Segment of hypotenuse2

The LEG is the Geometric mean between the HYPOTENUSE and the ADJACENT hypotenuse segment

Leg2 = Hypotenuse x Segment of hypotenuse adjacent to leg

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?

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).

From the similarity statement you found in the previous question, which ratio equals ? (Select all that apply.)

Altitude² = Segment of hypotenuse₁ x Segment of hypotenuse₂

Leg² = Hypotenuse x Segment of hypotenuse adjacent to leg

From the similarity statement you found in the previous question, which ratio equals
? (Select all that apply.)

Altitude² = Segment of hypotenuse₁ x Segment of hypotenuse₂

Leg² = Hypotenuse x Segment of hypotenuse adjacent to leg

From the similarity statement you found in the previous question, which ratio equals
? (Select all that apply.)