G8Q4 L03 - HINGE THEOREM & ITS CONVERSE

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Word Cloud

Describe in one word how you are feeling today!

QUICK RECALL

Work independently at voice level 1 to answer the questions on the next slides as a review of our previous discussions.

Multiple Choice

Would the set of numbers 11, 9, and 20 form the sides of a triangle?

• No
• Only if one side is longer
• They could form a right triangle
• Yes

Fill in the Blanks

Possible lengths for the third side of a triangle with sides 6 and 17.

Let x be the third side.

Dropdown

The sum of the lengths of any two ​

Select answer

of a triangle is ​

Select answer

the length of the ​ third ​ side.

Multiple Choice

Find x.

• 69 degrees

• 34 degrees

• 103 degrees

• 46 degrees

Dropdown

The measure of an exterior angle is ​

Select answer

any of its remote interior angles.

VERY GOOD!

WHAT'S NEW?

Today, let's learn another theorem about Triangles!

Austin and Adrian are hiking. They both started at the main station and walked in opposite directions for 20 meters. Then, Austin turned right at an angle of 40°, while Adrian also turned right at an angle of 80°. They each continued hiking for another 10 meters before stopping to rest.
Who is farther from the main station?

Poll

Who is farther from the main station?

• AUSTIN

• ADRIAN

Draw

CAN YOU ILLUSTRATE THE PROBLEM?

Austin and Adrian are hiking. They both started at the main station and walked in opposite directions for 20 meters. Then, Austin turned right at an angle of 40°, while Adrian also turned right at an angle of 80°. They each continued hiking for another 10 kimeters before stopping to rest.

1. How do you think the angle of their turn affects their final position?

   
   

2. Adrian turned at a larger angle than Austin. What do you think happens to the distance they traveled from the starting point?

THE HINGE THEOREM

a movable joint or mechanism on which a door, gate, or lid swings as it opens and closes or which connects linked objects.

Learning Targets

1. ​I can illustrate the Hinge Theorem and its Converse

2. I can solve real-life problems involving triangles using the Hinge Theorem and its converse.

3. I can cite real-life situations involving Hinge Theorem and its converse.

Open Ended

In your own words, how would you rephrase our learning targets today?

1. I can illustrate the Hinge Theorem and its Converse

2. I can solve real-life problems involving triangles using the Hinge Theorem and its converse.

3. I can cite real-life situations involving Hinge Theorem and its converse.

ACTIVITY 5.
Exploring the Hinge Theorem with GeoGebra

In this activity you will discover and generalize the Hinge Theorem and its Converse through hands-on exploration and observation. In your group in 10 minutes, you will be given a worksheet for you to work on.

ACTIVITY 5

When I say GO, follow the hand signals below and go to your group at Voice Level 1. Each group will be given worksheets.

ACTIVITY 5.
Exploring the Hinge Theorem with GeoGebra

When I say go, scan the QR code on your worksheet to start the activity. Work at voice level 2 and complete the task in 10 minutes.

Home

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What do you notice about the length of the opposite side as the angle increases?

What happens when the angle decreases?

Open Ended

(Question 3) Complete the statement.

If two sides of a triangle are congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second, then …

THE HINGE THEOREM

If two sides of a triangle are congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

THE HINGE THEOREM

Open Ended

(Question 4) Complete the statement.

If two sides of a triangle are congruent to two sides of another triangle and the third side of the first is longer than the third side of the second, then …

CONVERSE OF THE HINGE THEOREM

If two sides of a triangle are congruent to two sides of another triangle and the third side of the first is longer than the third side of the second, then the included angle in the first triangle is greater than the included angle in the second triangle.

CONVERSE OF THE HINGE THEOREM

Austin and Adrian are hiking. They both started at the main station and walked in opposite directions for 20 kilometers. Then, Austin turned right at an angle of 40°, while Adrian also turned right at an angle of 80°. They each continued hiking for another 10 kilometers before stopping to rest.
Who is farther from the main station?

Multiple Choice

Who is farther from the main station?

• AUSTIN

• ADRIAN

ACTIVITY 6.
LET’S PRACTICE!

When I say go, work independently at voice level 0 to determine which segment is longer in each given figure by applying the The Hinge Theorem and its Converse.

Multiple Choice

• CA

• CD

Multiple Choice

• HI

• HG

Multiple Choice

• ∠CBD

• ∠ACB

Poll

Learning Target Revisit:

Can you now illustrate the Hinge Theorem and its converse?

• Yes, I can do this independently and confidently.

• Yes, but I still need some guidance.

• No, I find this challenging and need more practice.

• No, I don’t understand this yet.

Poll

Learning Target Revisit:

Can you now solve real-life problems involving triangles using the Hinge Theorem and its converse?

• Yes, I can do this independently and confidently.

• Yes, but I still need some guidance.

• No, I find this challenging and need more practice.

• No, I don’t understand this yet.

Poll

Learning Target Revisit:

Can you cite real-life situations where the Hinge Theorem and its converse apply?

• Yes, I can do this independently and confidently.

• Yes, but I still need some guidance.

• No, I find this challenging and need more practice.

• No, I don’t understand this yet.

Open Ended

The three things that I have learned today are ...

Open Ended

The two things that I want to know more are ...

Open Ended

The one question I have is that ...

ASSIGNMENT

Which Door is More Convenient?

1. Pick two doors at home (e.g., bedroom vs. main door).

2. Estimate or measure:

• The two fixed side lengths (hinge to edge).

• The angle at which each door opens.

• The distance from the door’s edge to the wall (third side).

3. Compare the doors using the Hinge Theorem:

• Which door creates a longer third side?

• Which one allows for easier passage?

4. Explain your answer and suggest the best door opening angle for small spaces.