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Warm Up

Prove Triangles Similar by SSS and SAS. Warm Up. Lesson Presentation. Lesson Quiz. 1. ABC : m A = 90º, m B = 44º; DEF : m D = 90º, m E = 46º. similar. ANSWER. 2. ABC : m A = 132º, m B = 24º; DEF : m D = 90º, m F = 24º. not similar. ANSWER. Warm-Up.

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Warm Up

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  1. Prove Triangles Similar by SSS and SAS Warm Up Lesson Presentation Lesson Quiz

  2. 1.ABC: mA =90º, mB =44º;DEF:mD= 90º,mE= 46º. similar ANSWER 2.ABC: m A = 132º, m B = 24º; DEF : m D = 90º, m F= 24º. not similar ANSWER Warm-Up Determine whether the two triangles are similar.

  3. x– 1 6 3.Solve = . 8 12 5 ANSWER Warm-Up

  4. = = = = 8 12 AB 4 BC CA 4 16 4 Is either DEF or GHJsimilar to ABC? FD 9 12 3 3 EF 3 6 DE All of the ratios are equal, so ABC~DEF. Compare ABCand DEFby finding ratios of corresponding side lengths. = = Example 1 SOLUTION Shortest sides Longest sides Remaining sides

  5. 1 = = = = 16 AB 12 8 6 BC CA The ratios are not all equal, so ABCand GHJare not similar. JG 10 GH 16 8 HJ 5 Compare ABCand GHJby finding ratios of corresponding side lengths. 1 = = Example 1 Shortest sides Longest sides Remaining sides

  6. Find the value of xthat makes ABC ~ DEF. ALGEBRA 4 x–1 4 18 = 12(x – 1) 12 18 STEP1 Find the value of xthat makes corresponding side lengths proportional. = Example 2 SOLUTION Write proportion. Cross Products Property 72 = 12x – 12 Simplify. 7 = x Solve for x.

  7. ? = = 6 4 AB AC 4 AB BC 8 STEP2 Check that the side lengths are proportional when x = 7. 18 12 24 DF 12 DE DE EF ? = = Example 2 BC = x – 1 = 6 DF = 3(x + 1) = 24 When x = 7, the triangles are similar by the SSS Similarity Theorem.

  8. ANSWER MLN ~ZYX Guided Practice 1.Which of the three triangles are similar? Write a similarity statement.

  9. 15, 16.5 ANSWER Guided Practice 2. The shortest side of a triangle similar toRSTis 12 units long. Find the other side lengths of the triangle.

  10. Lean-to Shelter You are building a lean-to shelter starting from a tree branch, as shown. Can you construct the right end so it is similar to the left end using the angle measure and lengths shown? Example 3

  11. Both m A andm F equal = 53°, so A F. Next, compare the ratios of the lengths of the sides that include A and F. So, by the SAS Similarity Theorem, ABC~FGH. Yes, you can make the right end similar to the left end of the shelter. The lengths of the sides that include Aand F are proportional. 15 AB 3 3 9 AC = = FG 2 6 10 2 FH ~ = = Example 3 SOLUTION Shorter sides Longer sides

  12. 9 3 CA 3 18 BC 5 CD EC 15 30 5 = = = = The corresponding side lengths are proportional. The included angles ACB and DCEare congruent because they are vertical angles. So, ACB ~DCE by the SAS Similarity Theorem. Example 4 Tell what method you would use to show that the triangles are similar. SOLUTION Find the ratios of the lengths of the corresponding sides. Shorter sides Longer sides

  13. Explain how to show that the indicated triangles are similar. 3. SRT ~ PNQ ANSWER R  Nand == , therefore the triangles are similar by the SAS Similarity Theorem. 4 SR RT 3 PN NQ Guided Practice

  14. Explain how to show that the indicated triangles are similar. 4. XZW ~ YZX XZ WZ 4 WX XY XZ 3 YZ ANSWER WZX  XZYand = = = therefore the triangles are similar by either SSS or SAS Similarity Theorems. Guided Practice

  15. 1. Verify that ABC ~ DEF for the given information. ABC : AC = 6, AB = 9, BC = 12; DEF : DF = 2, DE= 3, EF = 4 AC AB BC 3 EF 1 DF DE ANSWER . The ratios are equal, = = = so ABC ~ DEF by the SSS Similarity Theorem. Lesson Quiz

  16. 2.Show that the triangles are similar and write a similarity statement. Explain your reasoning. = XY YZ 3 AB BC 4 ANSWER = = andYB . So XYZ ~ ABC by the SAS Similarity Theorem. Lesson Quiz

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