Triangle Proportionality Theorem Notes

Applying the Triangle Similarity Theorems

by Coach Miller

Multiple Choice

Two objects that are the same shape but not the same size are _______.

• Congruent
• Vertical
• Similar
• Complementary 

Multiple Choice

All corresponding angles in similar figures are congruent.  

• True
• False

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

Are the triangles similar? If yes, what did you use.

• Yes, by AA ~

• Yes, by SAS ~

• Yes, by SSS ~

• Not Similar

Multiple Choice

Determine if the two figures are similar or not using common ratios.

• No, the ratios between corresponding sides are different.

• No, because the sides aren't equal.

• Yes, because all the ratios are 4 to 1

• Yes, because all the ratios are 8 to 1

Multiple Choice

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar

Multiple Choice

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Open Ended

Essential Question: What information do you use to prioritize two triangles to determine if they are similar?

​Notes

​Converse of Side-splitter theorem

​If a line divides two sides of a triangle proportionally, then it is parallel to the remaining side

​Notes

Multiple Choice

Using the side-splitter theorem, which segment length would complete the proportion? $$\frac{GH}{HE}=\frac{?}{JF}$$  

• GF

• JH

• GJ

• EF

Multiple Choice

Using the side-splitter theorem, Daniel wrote a proportion for the segments formed by line segment DE. What is EC?

• 2 unit

• 2.4 units

• 3 units

• 3.75 units

Multiple Choice

What is the length of DC? Set up a proportion to solve

• 2 units

• 3 units

• 6 units

• 9 units

Fill in the Blanks

What is the length of GD? Hint: since the lines are parallel, the triangles are similar. Set up a proportion to solve

Midpoint - the half-way point of a line segment

​pause for paper folding activity

​Notes

Multiple Choice

To prove part of the triangle midsegment theorem using the diagram, which statement must be shown? Ignore the ordered pair stuff

• The length of JK equals the length of JL.

• The length of GH is half the length of KL.

• $$MN\ =\ \frac{1}{2}KJ$$  

• The slope of GH is half the slope of KL

Fill in the Blanks

What is the distance between points M & N?

Multiple Select

Which statements about triangle JKL are true? Select two options.

• M is the midpoint of line segment KJ.

• N is the midpoint of line segment JL.

• $$MN\ =\ \frac{1}{2}KJ$$  

• MN = 4.4

• MN = ML

Fill in the Blanks

What is the perimeter of triangle JKL?