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Proving Similar Triangles Chapter 7 – Lesson 3 Proving Similar Triangles

Objective: The students will be able to solve problems and prove triangles similar by using SSS~, and SAS~.

Verify that the triangles are similar. Example 1: Verifying Triangle Similarity Verify that the triangles are similar. ∆PQR and ∆STU Therefore ∆PQR ~ ∆STU by SSS~.

Verify that the triangles are similar. Example 2: Verifying Triangle Similarity Verify that the triangles are similar. ∆DEF and ∆HJK H  D def.  angles     Therefore ∆DEF ~ ∆HJK by SAS~.

Example 3: Writing Proofs with Similar Triangles Given: 3UT = 5RT and 3VT = 5ST Prove: ∆UVT ~ ∆RST Statements Reasons 1. 3UT = 5RT; 3VT = 5ST 1. Given 2. and 2. Division 3. 3. Substitution 4. RTS  VTU 4. Vert. s Thm. 5. ∆UVT ~ ∆RST 5. SAS ~

Example 4: Proving Triangles Are Similar Given: E(–2, –6), F(–3, –2), G(2, –2), H(–4, 2), and J(6, 2). Prove: ∆EHJ ~ ∆EFG by SAS~. Step 1 Plot the points and draw the triangles. Step 2 Use the Distance Formula to find the side lengths. The scale factor is 2:1.

Step 3 Find the scale factor. Example 4 Continued Step 3 Find the scale factor. = 2 = 2 Since and E  E, by the Reflexive Property, ∆EHJ ~ ∆EFG by SAS ~ .

Your Turn Graph the image of ∆ABC after a dilation with scale factor Verify that ∆A'B'C' ~ ∆ABC. Step 1 Multiply each coordinate by to find the coordinates of the vertices of ∆A’B’C’. Step 2 Graph ∆A’B’C’.

Step 2 Graph ∆A’B’C’. B’ (2, 4) A’ (0, 2) C’ (4, 0)

Step 3 Use the Distance Formula to find the side lengths. The scale factor is 2:3.

Step 4 Find the scale factor. Since , ∆ABC ~ ∆A’B’C’ by SSS ~.

Kahoot!

Lesson Summary: Objective: The students will be able to solve problems and prove triangles similar by using SSS~, and SAS~.

Preview of the Next Lesson: Objective: The students will review for Lesson 7-1 to 7-4 test.

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