Unit 6 Lesson 6.5: Triangle Similarity Theorems

​Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Find the length of BE, if possible.​

​First we have to determine whether or not these triangles are similar.

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If the triangles ARE similar, you CAN find BE.

If the triangles ARE NOT similar, you CANNOT find BE.

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Step 2: ​Use a theorem/postulate to determine if any are congruent.

• ​If you look at the indicators, we have PARALLEL LINES and two TRANSVERSALS.

• Parallel Lines & Transversals means we have:

  • SSIA (Same-Side Interior Angles)

  • AIA (Alternate Interior Angles)

  • AEA (Alternate Exterior Angles)

  • VA (Vertical Angles)

  • CA​ (Corresponding Angles)

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​#1

​#2

​#3

​#1

​#2

​#3

Step 3: Solve the proportion. ​

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​Theorem: If all 3 sides of one triangle are proportional to all 3 sides of another triangle, then the two triangles are similar.

​Theorem: If 2 sides of one triangle are proportional to 2 sides of another triangle and their included angles are congruent, then the two triangles are similar.

Determine whether the given triangles are similar.  Justify your reasoning using a triangle similarity theorem.

Determine whether the given triangles are similar.  Justify your reasoning using a triangle similarity theorem.

Step 2: Determine which theorem you can use (process of elimination).

​AA (must have info for at least 2 angles)

SSS (must have info for all 3 sides)​

SAS (must have info for 2 sides and an angle in between)

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Step 3: Check angle measures & ratios.

They aren't similar yet. Use those charts like we did in Unit 5!

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