Unit IIA Day 5

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8.5 Proving Triangles are Similar

• Unit IIA Day 5

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Do Now

• In the figure below, find a pair of similar
  triangles and use them to answer the questions.
• Write a statement of similarity for the two
  triangles.
• Explain how you know that the two triangles are
  similar.
• Find MQ.

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Side Side Side (SSS) Similarity Theorem

• If the corresponding sides of two triangles are
  proportional, then the triangles are similar.
• If _____________________, then ?ABC ?PQR.

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Ex. 1 Proof of SSS Similarity

• Locate P on RS so that PS LM. Draw PQ so that
  PQ RT.

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Ex. 2 Using the SSS Similarity Thm.

• Which of the three triangles are similar?

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Side Angle Side Similarity Thm.

• If an angle of one triangle is congruent to an
  angle of a second triangle and the lengths of the
  sides including these angles are proportional,
  then the triangles are similar.
• If ________ and ______________, then ?XYZ ?MNP.

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Ex. 3 Using the SAS Similarity Thm.

• GIVEN SP 4, PR 12, SQ 5, and QT 15
• PROVE ?RST ?PSQ

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Ex. 4 Using a Pantograph

• In the figure below, the drawing of a daisy has
  been enlarged in such a way that P, B, and D and
  P, A, and C are collinear and PB/PD PA/PC.
• How do you know that ?PDC ?PBA ?
• In the diagram, PA 8 in. and AC 8 in. The
  diameter of the original daisy is 1.8 in. What is
  the diameter of the daisy in the enlargement?

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Closure

• State the two similarity theorems presented in
  this lesson.