1 / 16

Similarity

Similarity. Triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. TESTS FOR SIMILARITY. Two triangles are similar if: All corresponding angles are equal All the corresponding sides have the same ratio (proportional).

urbain
Download Presentation

Similarity

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. Similarity

  2. Triangles are similar if their corresponding angles are equal and their corresponding sides are proportional TESTS FOR SIMILARITY Two triangles are similar if: • All corresponding angles are equal • All the corresponding sides have the same ratio (proportional)

  3. How To Identify？ Two triangles are similar if: • 3 angles of 1 triangle are the same as 3 angles of the other • 3 pairs of corresponding sides are in the same ratio • 2 pairs of corresponding sides are in the same ratio and the included angle is equal

  4. Tests for similarity of 2 triangles Type 1: 3 angles of 1 triangle are the same as 3 angles of the other(AAA) D A In triangle ABC, any 2 angles are equal to any 2 angles of triangle DEF, then they are similar. k g l j i h F E C B Angle g= angle k Angle h= angle j Angle i= angle l  triangle ABC and DEF are similar

  5. Test for similarity between 2 triangles Type 2: 3 pairs of corresponding sides are in the same ratio D A In triangle ABC and DEF, if z i kz ki where k is a constant. B C h F E kh  triangle ABC and DEF are similar.

  6. Tests for similarity between two triangles Type 3:2 pairs of corresponding sides are in the same ratio and the included angle is equal (SAS) D A In triangle ABC and DEF, if kz z i ki g and angle g = angle h. C h B h F E kh  triangle ABC and triangle DEF are similar.

  7. Question • Are the following triangles similar? Not drawn to scale. A D 40 40 75 E 65 B F C

  8. Question • Are the following triangles similar? Not drawn to scale. D A 12 6 4 2 F C B E 10 5

  9. Question • Are the following triangles similar? Not drawn to scale. A D 7.5 3.5 2 1 B F B 4 E 5

  10. Question • Are the following triangles similar? Not drawn to scale. D A 3.5 10 55 55 F C B 5 E 7

  11. Think! Which of the following triangles are always similar? a.  right triangles b.  isosceles triangles c.  equilateral triangles 1

  12. 2. Similar triangles are exactly the same shape and size. A) True B) False

  13. 3. The sides of a triangle are 5, 6 and 10.  Find the length of the longest side of a similar triangle whose shortest side is 15. A)10 B)15 C)18 D)30

  14. In the diagram, DE is parallel to AC.  BD = 4, DA = 6 and EC = 8.  Find BC to the nearest tenth. 4. • 4.3 • 5.3 • 8.3 • 13.3

  15. Find BC. 5. • 4 • 4.5 • 13.5 • 17

  16. At a certain time of the day, the shadow of a 5' boy is 8' long.  The shadow of a tree at this same time is 28' long.  How tall is the tree? 6. • 8.6 • 16 • 17.5 • 20

More Related