Download Section 6.2 Similar Triangles (Recall: similar figures have the same

Section 6.2 Similar Triangles
(Recall: similar figures have the same shape, but not the same size.)
All squares are similar to each other...All circles are similar to each other.
However, not all triangles are similar. There are many applications of similar triangles in finding distances, etc. Similar Triangles: ABC is similar to DEF if and only if
• All three pairs of corresponding angles are congruent.
• All pairs of corresponding sides are proportional. (written ABC ~ DEF )
<A ≅ <D <B≅ <E <C≅ <F and
AB = BC = AC
DE EF DF
(Note that the following properties for congruent triangles also hold for similar triangles):
• Reflexive
• Symmetric
• Transitive
Look at Example 6.8 on page 308:
AAA Similarity Postulate: Two triangles are similar if and only if three angles of one triangle are congruent, respectively, to three angles of the other triangle.
B
E
250
250
D
950
950
F
C
A
AA Similarity Theorem: Two triangles are similar if two angles of one triangle are congruent, respectively, to two angles of the other triangle.
Practice: D
A
B
E
C
Given: DE is parallel to AC;
AB = 6 CE = 1 AC = 8
BE = x BD = 4
Find: a) DE
b) BC
Corollary: Two right triangles are similar if an acute angle of one triangle is congruent to an acute angle of the other triangle.
SAS Similarity Theorem: Two triangles are similar if two sides of one triangle are proportional, respectively, to two sides of another triangle and the angles included between the sides are congruent. (use similar markings)
(See Example 6.10 on page 311)
LL Similarity: Two right triangles are similar if the legs of one triangle are proportional respectively to the legs of the other triangle.
SSS Similarity: Two triangles are similar if three sides of one triangle are proportional to three sides of the other triangle.
(read together Example 6.11 on page 312)