Similarity

TESTS FOR SIMILARITY Two triangles are similar if: All corresponding angles are equal All the corresponding sides are proportional Triangles are similar if their corresponding angles are equal and their corresponding sides are proportional

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

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 angle is equal to any 2 angles of triangle DEF, then they are similar. k g l j i h F C E B Angle g= angle k Angle h= angle j Angle i= angle l  triangle ABC and DEF are similar

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.

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.

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

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

Question Are the following triangles similar? Not drawn to scale. A D 7.5 3.5 2 1 B F B 4 E 5 Ans: no

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

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

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

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 Ans:D

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

Find BC. 5. 4 4.5 13.5 17 Ans:C

At a certain time of the day, the shadow of a 5' boy is 8' long 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 Ans:C