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Proving Triangles Similar

Proving Triangles Similar. Geometry Extra Credit Nina & Salihe. Similar Shapes. Same Shape (Angles) Different Size (Sides). Forcing Similarity. AA AA The symbol for similarity: ~ ∆ABC ~ ∆DEF. Proving Triangles Similar. D. E. C. Given : ABCD is a parallelogram

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Proving Triangles Similar

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  1. Proving Triangles Similar Geometry Extra Credit Nina & Salihe

  2. Similar Shapes • Same Shape (Angles) • Different Size (Sides)

  3. Forcing Similarity • AA AA • The symbol for similarity: ~ • ∆ABC ~ ∆DEF

  4. Proving Triangles Similar D E C Given: ABCD is a parallelogram EB perpendicular to DC BF perpendicular to AD Prove: ∆BAF ~ ∆BCE F A B 1. ABCD is a parallelogram Given < A is to < C In a parallelogram, opposite angles are 3. BE is perpendicular to CD Given 4. BF is perpendicular to AD Given 5. < BAF and <BCE are right angles Perpendicular lines form right angles 6. < BAF < BCE Right angles are AA ~ AA 7. ∆BAF ~ ∆BCE

  5. Rule • If two triangles are similar, their corresponding sides are in proportion. 4 4 2 2 2 1

  6. Proportionate Sides • Find the value of x if AB=16, FB=14, and BC=12. (∆ABF ~ ∆CEB) D E C F x 12 14 A B 16 14 16 X 12 16 X=168 X = 10.5 =

  7. Now You Try Given: WA||CH WH and AC intersect at point T Prove: ∆WAT ~ ∆CTH

  8. Continued…. • In the diagram below of ∆PRT, Q is a point on PR and S is a point on TR, QS is drawn, and <RPT <RSQ. Which reason justifies the conclusion that ∆PRT ~ ∆SRQ? (1) AA (3) SAS (2) ASA (4) SSS

  9. Homework

  10. Thank You

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