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Similar Triangles

Similar Triangles. Similar Triangles Formal Definition. Two Triangles are similar if and only if all three corresponding internal angles are congruent . Similar Triangles Formal Definition. Two Triangles are similar if and only if all three corresponding internal angles are congruent .

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Similar Triangles

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  1. Similar Triangles

  2. Similar Triangles Formal Definition • Two Triangles are similar if and only if all three corresponding internal angles are congruent

  3. Similar Triangles Formal Definition Two Triangles are similar if and only if all three corresponding internal angles are congruent

  4. Do we need to know all 6 anglesto prove triangles similar • Remember the sum of the interior angles of a triangles always equals 180 degrees • So if we know two angles we know the third • If 2 pairs of internal angles are congruent the third pair is also

  5. AA Postulate • If 2 pairs of internal angles are congruent the third pair is also • Therefore if two triangles have two corresponding angles congruent the triangles are similar

  6. AA Postulate

  7. Definition Corresponding Sides • The side in each triangle opposite the congruent angle. What?

  8. Definition Corresponding Sides One side in each triangle that is opposite the congruent angle The side in each triangle opposite the congruent angle

  9. Similar Triangles 90/45=2 If two triangles are similar then the ratios of the corresponding sides are equal 100/50=2 80/40=2 If two triangles are similar then the ratios of the corresponding sides are equal We say the corresponding sides are proportional

  10. Remember your work with ratios a/x=b/y Then we cross multiply ay=bx Divide a/b=x/y Therefore If two triangles are similar then the ratio between any two sides of one triangle is equal to the ratio between the corresponding sides in the other triangles. We say corresponding pairs are proportional

  11. Similar Triangles 90/100=45/50 80/100=40/50 If two triangles are similar then the ratio between any two sides of one triangle is equal to the ratio between the corresponding sides in the other triangles We say corresponding pairs are proportional 90/80=45/40

  12. Pickup a set of instructions Go to the computer Click The Geometer's Toolkit ICON Open the Similar Triangles Tool Follow the instructions on the sheet you picked up

  13. Similar Triangles and Transformations • Remember triangles remained congruent over reflection rotation and translation These transformations created congruent images. • Triangles also remain similar over reflection rotation transformation and can do under dilation. Dilation produces an image that is similar if the angles do not change. Click Here To See

  14. What Can we do with all this • We can use the information to find unknown parts of triangles • Tomorrow we will use what we learned to help us measure the height, length or width of various objects

  15. What Can we do with all this

  16. What Can we do with all this

  17. What Can we do with all this

  18. An Easy Way to Keep Track You Can take You Ratios either Horizontally or Vertically Make a Chart 4/y=8/(y+4) or 4/8=y/(y+4) Cross Multiply 4(y+4)=8y 4 8 Divide by 4 y+4=2y y y+4 Subtract y 4=y or y=4

  19. 4/y=8/y+4 or 4/8=y/y+4 Cross Multiply 4(y+4)=8y 4 8 Divide by 4 y+4=2y y y+4 Subtract y 4=y or y=4

  20. Links you may find helpful http://www.mathopenref.com/similartriangles.html A great quick reference (you saw it earlier) http://www.glencoe.com/sec/math/brainpops/00112049/00112049.html A preview of tomorrowhttp://library.thinkquest.org/20991/geo/spoly.html “Math for Morons” always a good choice

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