section 8.3 proving triangles similar by: asad ashraf
TRANSCRIPT
![Page 1: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/1.jpg)
Section 8.3Proving Triangles Similar
By: Asad Ashraf
![Page 2: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/2.jpg)
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**
![Page 3: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/3.jpg)
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~.
![Page 4: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/4.jpg)
AAA~ Postulate
• AAA~ Postulate - If three angles of one triangle are congruent to three angles of a 2nd triangle then the triangles are similar.
![Page 5: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/5.jpg)
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.
![Page 6: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/6.jpg)
SSS~ Theorem
• SSS~ If 3 sides of one triangle are proportional to three sides of a 2nd triangle then the two triangles are similar.
![Page 7: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/7.jpg)
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.
![Page 8: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/8.jpg)
Sample Problems
• Click Here• SSS~ and SAS~ Problems
![Page 9: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/9.jpg)
Sample ProblemsAre these triangles ~?
Answer: Yes they are because Included angles were given congruent and the ratios of the sides are congruent as well.
![Page 10: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/10.jpg)
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
![Page 11: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/11.jpg)
Practice Problems
• Are any 2 isosceles triangles similar? Show all work.
![Page 12: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/12.jpg)
Practice Problems
• Are these triangles similar? Why or why not?
Answer: NO
![Page 13: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/13.jpg)
Practice Problems
• Given: XS and RY are Altitudes of RTS
• Prove: Triangle TSX is similar to Triangle TYR
![Page 14: Section 8.3 Proving Triangles Similar By: Asad Ashraf](https://reader036.vdocuments.mx/reader036/viewer/2022062407/56649f3e5503460f94c5e0e5/html5/thumbnails/14.jpg)
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%20Webs/Geometry/chpt8.htm#Test%20Review%20-%20%20Chapter%208.1-4>.