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SIMILAR TRIANGLES

SIMILAR TRIANGLES. LESSON 18(2). SIMILAR TRIANGLES. Similar is a mathematical word meaning the same shape. We say that two triangles , triangle FDE and triangle LMK, are similar if the ratio of each side is similar. FD : DE : EF = LM : MK : KL. SIMILAR TRIANGLES.

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SIMILAR TRIANGLES

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  1. SIMILAR TRIANGLES LESSON 18(2)

  2. SIMILAR TRIANGLES Similar is a mathematical word meaning the same shape. We say that two triangles , triangle FDE and triangle LMK, are similar if the ratio of each side is similar. FD : DE : EF = LM : MK : KL

  3. SIMILAR TRIANGLES This equation of two three term ratios can also be written in fraction form: FD LM DE MK EF KL = = Corresponding sides are equal NOTE: All sides of one triangle must be either all in the numerator or denominator.

  4. SIMILAR TRIANGLES In similar triangles, corresponding angles are equal. • F =  L • D =  M • E =  K IMPORTANT: If you know two triangles are similar, then their corresponding angles are equal. Conversely, if two triangles have equal corresponding angles, then the triangles are similar.

  5. EXAMPLE 1 Prove the two triangles are similar? SOLUTION: • Angles: • A =  D • B =  E • C =  F Sides: AB DE BC EF AC DF = = 8 12 6 9 5 7.5 = = 540 810 540 810 540 810 = = Since corresponding angles are equal, then corresponding sides are equal. Therefore the two triangles are similar.

  6. YOU TRY! Prove the two triangles are similar? SOLUTION: Angles: Sides:

  7. SOLUTION Prove the two triangles are similar? SOLUTION: • Angles: • M =  O • L =  P • N =  Q Sides: ML OP MN OQ LN PQ = = 4 12 6 18 3 9 = = 12 36 12 36 12 36 = = Since corresponding angles are equal, then corresponding sides are equal. Therefore the two triangles are similar.

  8. EXAMPLE 2 Find the measures of  A,  B,  C. SOLUTION: Sides: Since the ratios of the sides are all equal, the triangles are similar, that also means the corresponding angles are equal. FH AC FG AB GH BC = = 42 3.5 7 3 6 5.3 10.6 = = 1 2 1 2 1 2 = = Therefore:  F =  A  H =  C  G =  B • A = 100o • C = 38o • B = 42o

  9. YOU TRY! Find the measures of  M,  L,  K. SOLUTION: Sides: 17

  10. SOLUTION Find the measures of  M,  L,  K. SOLUTION: Sides: Since the ratios of the sides are all equal, the triangles are similar, that also means the corresponding angles are equal. ML AB MK AC LK BC = = 16 4 20 5 18 4.5 = = 4 = 4 = 4 17 Therefore:  M =  A  L =  B  K =  C • M = 105o • L = 17o • K = 58o

  11. Triangle ABC is similar to Triangle RPQ. Find the lengths of RP and AC AB RP BC PQ AC RQ = = EXAMPLE 3 SOLUTION: Sides: 8 x 12 16.8 y 21 = = 8 x 12 16.8 12 16.8 y 21 = = 12x = 8(16.8) x = 16.8y = 12(21) y = 134.4 12 252 16.8 RP = 11.2 AC = 15

  12. Triangle SIP is similar to Triangle MAT. Find the lengths of MA and SP YOU TRY! SOLUTION: Sides:

  13. Triangle SIP is similar to Triangle MAT. Find the lengths of MA and SP SI MA SP MT IP AT = = SOLUTION SOLUTION: Sides: 7 x y 17.3 13 25 = = 7 x 13 25 13 25 y 17.3 = = 13x = 7(25) x = 25y = 13(17.3) y = 175 13 224.9 25 MA = 13.5 SP = 9

  14. For the figure below, show that Triangle DEF is similar to Triangle DGH. EXAMPLE 4 SOLUTION: • If two triangles have equal corresponding angles, then the triangles are similar. • Therefore: • D =  D ( common angle) • E =  G (Corresponding angles) • F =  H ( corresponding angles ) Therefore: Triangle DEF is similar to Triangle DGH.

  15. Class work • Check solutions to Lesson 18. • Copy down notes and examples • Do Lesson 18(2) worksheet.

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