SIMILAR TRIANGLES

1. SIMILAR TRIANGLES LESSON 18(3)

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: • K =  A • L =  B • M =  C Sides: KL AB KM AC LM BC = = 8 12 10 15 6 9 = = 1080 1620 1080 1620 1080 1620 = = 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: • L =  K • M =  S • O =  T Sides: LM KS LO KT MO ST = = 4 5 5 6.25 6 7.5 = = 187.5 234.38 187.5 234.38 187.5 234.38 = = Since corresponding angles are equal, then corresponding sides are equal. Therefore the two triangles are similar.

8. 3 9 4 y = 3 9 x 12 = EXAMPLE 2 Solve for the unknown values. SOLUTION: Sides: • Angles: • A=  E • B =  D • C= C AB DE BC DC AC EC = = 3 9 4 y x 12 = = 9(4) = 3y 36 = 3y 12 = y 3(12) = 9x 36 = 9x 4 = x

9. YOU TRY! Solve for the unknown values. SOLUTION: Sides: Angles:

10. 6 9 3 y = 6 9 x 12 = SOLUTION Solve for the unknown values. SOLUTION: Sides: • Angles: • C=  P • T =  R • Z= Z CT PR TZ RZ CZ PZ = = 6 9 3 y x 12 = = 9(3) = 6y 27 = 6y 4.5 = y 6(12) = 9x 72 = 9x 8 = x

11. Class work • Copy down examples • Finish Lesson 18(2) worksheet.