Similar Triangles

Similar Triangles

​guided lesson

by Erica Player

Let's discuss SIMILAR triangles!

What do you notice about the angles?

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​What might the side lengths be? Let's make up some side measure that make sense...

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​*TAKE NOTES ON PAPER*

A similarity statement shows which angles are CORRESPONDING and CONGRUENT.

Multiple Choice

 Complete the statement:

$$\Delta BAC\sim\Delta$$  _____

• FED

• EDF

• DEF

• FDE

Multiple Choice

 Complete the statement:

$$\Delta BAC\sim\Delta$$  _____

• FED

• DEF

• EDF

• FDE

Multiple Choice

What is the similarity statement for the triangle pair?

• ΔXYZ~ΔNEW
• ΔXZY~ΔNWE
• ΔYZX~ΔNWE

Poll

Rate your understanding of WRITING SIMILARITY STATEMENTS.

​When triangles are SIMILAR, all corresponding angles are _________, and all corresponding sides are ___________.

Multiple Choice

Sides in similar figures must be proportional.  

• True
• False 

Multiple Choice

If two figures are similar their angles are______.

• proportional
• congruent
• supplementary
• complementary

Multiple Choice

If two figures are similar, the corresponding sides are ______________.

• equal
• congruent
• proportional
• none of these

When at least 2 pairs of corresponding angles are congruent, the triangles must be similar. See examples below.

​Sometimes, both pairs of angles are not marked for you. We must mark them in the picture.

​​*TAKE NOTES ON PAPER*

Multiple Choice

Are these triangles similar?

• Yes, by AA

• No

• not enough information

• Yes, by SAS

​Sometimes, you don't need to know any angles...

IF you can determine ALL 3 sides are proportional

Multiple Choice

Check the proportions to determine if the triangles are similar by SSS.

• Yes, they are proportional

• They are NOT proportional

Multiple Choice

Check the proportions to determine if the triangles are similar by SSS.

• Yes, they are proportional

• They are NOT proportional

Multiple Choice

Check the proportions to determine if the triangles are similar by SSS.

• Yes, they are proportional

• They are NOT proportional

Poll

Rate your understanding of WRITING AND CHECKING SIDE RATIOS.

​One more shortcut...2 pairs of proportional sides and the included angle (in between)        SAS

​Is there at least 1 pair of congruent angles?

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​Are the angles IN BETWEEN the sides?

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​Do the 2 pairs of corresponding sides have the same ratio?

Multiple Choice

Check the side ratios. Are the triangles similar by SAS?

• YES

• NO

Multiple Choice

Is there enough information to justify similarity by SAS?

• No, because you need another pair of SIDES

• Yes, because you can mark the VERTICAL angles

• No, because you need ano pair of ANGLES

Multiple Choice

Is this SAS similarity?

• YES - 2 sides and the angle in between

• NO, because the angle is not IN BETWEEN the sides

• NO, this is SSS

• NO, this is AA

​10 Mixed Problems to try on your own...

Multiple Choice

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

• AA

• SAS

• SSS

• Not similar

Multiple Choice

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

• AA 

• SAS 

• SSS 

• Not similar

Multiple Choice

Complete the similarity statement: △CED ~ _______

• △VTU

• △TVU
  

• △UTV

Multiple Choice

Determine whether the triangles are similar(name the postulate or theorem you used).

• SSS similar
• AA similar
• SAS similar

Multiple Choice

If the triangles are similar, state how.

• SSS

• SAS

• AA

• Not similar

Multiple Choice

How are these triangles similar? 

• A
• B
• C
• D

Multiple Choice

If two figures are similar their angles are______.

• proportional
• congruent
• supplementary
• complementary

Multiple Choice

If two figures are similar, the corresponding sides are ______________.

• equal
• congruent
• proportional
• none of these

Multiple Choice

Which is not a similar triangle theorem?

• SS∼

• SAS∼

• SSS∼

• AA∼

Multiple Choice

State the postulate that proves these triangles are similar.

• AA~

• SAS~

• SSS~

• Not Similar

Poll

Rate your OVERALL understanding of the Similar Triangle Lesson