Download Section 8.3 Proving Triangles Similar

Section 8.3
Proving Triangles Similar
By: Asad Ashraf
What is Similarity
• Similar figures are figures in which the shape
is exactly the same, but the size is not.
• A Dilation is an enlargement of a figure. It is
still similar, however.
• A Reduction is a reduction of a figure. This is
also similar.
• **Remember that similar figures are not
necessarily congruent**
Proving Triangles Similar
• There are several methods to prove triangles
similar.
• These are very similar to the methods of
proving triangles congruent.
• The methods are AAA~, AA~, SAS~, and SSS~.
AAA~ Postulate
• AAA~ Postulate - If three angles of one
triangle are congruent to three angles of a 2nd
triangle then the triangles are similar.
AA~ Theorem
• AA~ if 2 angles of one
triangle are congruent
to two angles of a 2nd
triangle then the
triangles are similar.
• This is proved by the
No-Choice Theorem and
AAA~ Theorem
combined.
SSS~ Theorem
• SSS~ If 3 sides of one triangle are proportional
to three sides of a 2nd triangle then the two
triangles are similar.
SAS~ Theorem
• SAS ~ If two sides of
one triangle are
proportional to the
corresponding two
sides of a 2nd triangle
and their included
angles are congruent,
then the triangles are
similar.
Sample Problems
• Click Here
• SSS~ and SAS~ Problems
Sample Problems
Are these triangles ~?
Answer: Yes they are because
Included angles were given
congruent and the ratios of the
sides are congruent as well.
Practice Problems
• Prove that an acute angle of one right angle is
congruent to the vertex angle of an isosceles
triangle, they are similar.
• Always, Sometimes, Never
– If 2 triangles are similar, they are congruent ____
– If 2 triangles are congruent, they are similar ____
– 2 rectangles are similar if neither is a square ____
– 2 right triangles are similar____
Answers: A, S, S, S
Practice Problems
• Are any 2 isosceles triangles similar? Show all
work.
Practice Problems
• Are these triangles similar? Why or why not?
Answer: NO
Practice Problems
• Given: XS and RY are
Altitudes of RTS
• Prove: Triangle TSX is
similar to Triangle TYR
Works Cited
• Our Book
• “Similar Triangles”. Mathwarehouse.com. May
27,2008.<http://www.mathwarehouse.com/geometry/similar
/triangles/index.html>.
• “Chapter 8”. Teacherweb.org. 2003. May
27,2008.<http://teacherweb.ftl.pinecrest.edu/wingjoa/My%2
0Webs/Geometry/chpt8.htm#Test%20Review%20%20%20Chapter%208.1-4>.