# Discovering Triangle Similarity Theorems

- Author:
- Harrison Bosher, Mr. Bokar, Tim Brzezinski

- Topic:
- Angles

Recall when you learned about the properties of triangles. What is the sum of any triangles interior angles?

What do we notice about the about the angles of our two triangles? Do we know if the unmarked angles are also congruent, if so, explain how you know.

Compare the ratios of corresponding sides of our two triangles. What relationships do you notice? (Try multiple triangles to test multiple examples.)

Last class, we explored the properties of similar triangles. What were 2 properties we claimed that similar triangles have?

Using your observations from this explore, finish the following conjecture. Given two ________ have two pairs of congruent corresponding _________, then the two _________ are _______.

## Before Using the "Slide me" Slider.

Find the ratios of A and AK, B and BK, C and CK. Compare the ratios and describe your observations.

Using what we found above, how can we describe the corresponding sides of these two triangles? (Note: This is our given)

## Now use the "Slide me" Slider.

What did the animation show us about our two triangles?

What can we conclude about our two triangles and why can we conclude that? (What theorem can we use?)

Using the observations you made during this explore, finish the following conjecture by filling in the blanks. If 3 _____ of one ______ are in a ________ to 3 _______ of another _________, then those __________ are ________.

## PLACE RED SLIDER FULLY TO THE LEFT

Find the ratios of A and AK, B and BK. Compare the ratios and describe your observations. (Think about your vocabulary words, which one perfectly describes your observations?)

Before moving any sliders, describe what information is given by the model.

## NOW MOVE BOTH THE RED SLIDER AND BLUE SLIDER TO THE RIGHT.

What did the animation show us about our two triangles? (What new information did we find from the animation?)

What can we conclude about our two triangles and why can we conclude that? (What theorem can we use?)

Using the observations you made during this explore, finish the following conjecture by filling in the blanks. If one _____ of one triangle is ________ to one _______ of another _________, and the lengths of the _____ including these angles are ________, then the two ______ are ______.