1 / 28

Presentation on

Presentation on. Similar and Congruent Triangles By Farhan Iqbal DA SKBZ College. Objective. By the end of this lesson Students will understand the basic concepts of similarity and congruency

faolan
Download Presentation

Presentation on

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Presentation on Similar and Congruent Triangles By Farhan Iqbal DA SKBZ College

  2. Objective By the end of this lesson • Students will understand the basic concepts of similarity and congruency • Students will know how to determine that two figures are similar or congruent by investigating figures that are similar or congruent.

  3. Congruent The two polygons are said to be congruent if they are having the same shape and same size

  4. We use the symbol to represent the congruency of two figures

  5. Examples of Congruent Shapes

  6. Congruent figures can be rotations of one another.

  7. Congruent figures can be reflections of one another.

  8. C Z A X B Y Congruency of triangle When two triangles are congruent, all their corresponding sides and corresponding angles are equal. In the figure, if △ABC △XYZ, AB = XY,BC = YZ, CA = ZX. ∠A = ∠X, ∠B = ∠Y, ∠C = ∠Z, and

  9. Practice Time!

  10. Name all corresponding parts. ∆BAD is congruent to ∆THE D E A B T H

  11. ∆BAD is congruent to ∆THE Name all corresponding parts. D E A B T H ANGLES SIDES B T BA TH A H AD HE D E DB ET

  12. For two congruent triangles, their corresponding sides and angles are equal. ∴ , , ∴ p = 6 cm r = 50° q = 5 cm Given that △ABC△XYZ in the figure, find the unknowns p, q and r.

  13. ∆QRS is congruent to ∆BRX Name all corresponding parts. S R B Q X

  14. ∆QRS is congruent to ∆BRX Name all corresponding parts. S R B Q X ANGLES SIDES Q B QR BR S X QS BX R R SR XR

  15. ∆EFG is congruent to ∆FGH Name all corresponding parts. E H G F

  16. ∆EFG is congruent to ∆FGH Name all corresponding parts. E H G F ANGLES SIDES E H EF HF F F EG HG G G GF GF

  17. IH RS 3a = 6 3a = 6 3 3 In the figure, quadrilateral JIHK quadrilateral QRST. Find a. Divide both sides by 3. 3a I H a = 2 6 4b° S R 120° J 30° Q K c + 10° T

  18. H S 4b = 120 4b = 120 4 4 In the figure, quadrilateral JIHK quadrilateral QRST Find b. Divide both sides by 4. 3a I H 6 4b° S R b = 30° 120° J 30° Q K c + 10° T

  19. K T c + 10 = 30 In the figure, quadrilateral JIHK quadrilateral QRST. Find c. Subtract 10 from both sides. 3a I H 6 c = 20° 4b° S R 120° J 30° Q K c + 10° T

  20. Similar Figure Two figures having the same shape are called similar figures. The figures A and B as shown is an example of similar figures.

  21. Similar Figure • Two congruent figures must be also similar figures. • When a figure is enlarged or reduced, the new figure is similar to the original one.

  22. Similar Triangles If two triangles are similar, then • their corresponding angles are equal; • their corresponding sides are proportional.

  23. B In the figure, if △ABC ~ △XYZ, then ∠A = ∠X, ∠B = ∠Y, ∠C = ∠Z and . A C Y X Z Similar Figure

  24. Practice Time!

  25. ∴ = ∴ = z = In the figure, given that △ABC ~ △PQR, find the unknowns x, y and z. y = 98° x = 30° , = 7.5

  26. ∴ x = 90° In the figure, △ABC ~ △RPQ. Find the values of the unknowns. Since △ABC ~ △RPQ, ∠B = ∠P

  27. Also, Also, = = = z = = y = ∴ ∴ y = 36 z = 65

  28. Thank You

More Related