Unit IIA Day 5

8.5 Proving Triangles are Similar

Do Now

In the figure below, find a pair of similar triangles and use them to answer the questions.

1.Write a statement of similarity for the two triangles.2.Explain how you know that the two triangles are

similar.3.Find MQ.

Side Side Side (SSS) Similarity Theorem

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

Ex. 1: Proof of SSS Similarity

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

Ex. 2: Using the SSS Similarity Thm.

Which of the three triangles are similar?

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.

Ex. 3: Using the SAS Similarity Thm.

GIVEN: SP= 4, PR = 12, SQ = 5, and QT = 15;PROVE: ∆RST ~ ∆PSQ

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?

Closure

State the two similarity theorems presented in this lesson.