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## Side Angle Side Theorem

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**Side Angle Side Theorem**By Andrew Moser**Summary**• If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. • If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.**Web Links**• http://www.mathwarehouse.com/trigonometry/area/side-angle-side-triangle.html • http://hotmath.com/hotmath_help/topics/SAS-postulate.html • http://www.jimloy.com/cindy/ass.htm**Side Side Side**Kyle Schroeder**Summary**• You can only find SSS if the three sides in one triangle are congruent. • We learned this when using Solving Triangle Proofs**Rules, Properties, & Formulas**• The rule and property for SSS theorem is that you can only determine that you have reached SSS is that the triangle has to be congruent to the other triangle**Web Links**• http://www.cut-the-knot.org/pythagoras/SSS.shtml • http://www.tutorvista.com/topic/proof-of-sss-theorem • http://www.mathwarehouse.com/geometry/congruent_triangles/side-side-side-postulate.php**Proofs Involving CPCTCby, Nick Karach**Summary: -CPCTC stands for: “Corresponding Parts of Corresponding Triangles are Congruent” • This means that once you prove two triangle congruent, you know that corresponding sides and angles are congruent.**Rules, Properties & Formulas**• First of all you must prove the Triangles congruent through a postulate such as ASA, SAS, AAS or HL. • Second, once you state the two triangles are congruent, you can state a two sides are congruent. Ex.**Examples**Given:**Web Links**• Main Concept and Some Examples • CPCTC WikiPedia • Examples**Equilateral Triangle**By Jake Morra**Equilateral Triangles**• A equilateral triangle is a triangle where all the sides are equal in length. • All angles opposite though sides are congruent**Finding The Height**To find the height add an altitude from vertexes to opposite segment If Segment AB, BC, and CA are all 10 then Segment BP and PC are 5 If the added segment is a altitude. angle BPA and APC are 90 degrees a + 5 = 10 Now that you know all of this can solve the height by the Pythagorean Theorem**Other Websites To Help You**• http://mathcentral.uregina.ca/QQ/database/QQ.09.02/rosa2.html • www.calcenstein.com/calc/1111_help.php • www.ehow.com › Education › Math Education › Triangles**Angle Bisector and Incenter**What is an angle bisector and an incenter? Example problems Web links**What is an angle bisector and an incenter?**An angle bisector is a segment that divided an angle in half. When the three angle bisectors intersect they create a point of concurrency which is called the incenter**Ex: 2 Find x**Equation: 13x-1= 2(6x+4) 13x-1= 12x+8 -12x 12x x-1= 8 +1 +1 X= 9**Ex:3 Incenter is ALWAYS in the middle**Acute Right Obtuse**Helpful Links**• http://www.cliffsnotes.com/study_guide/Altitudes-Medians-and-Angle-Bisectors.topicArticleId-18851,articleId-18787.html • http://jwilson.coe.uga.edu/emt725/Prob.2.35.1/Problem.2.35.1.html • http://mathworld.wolfram.com/AngleBisector.html**Angle Side Angle Theorem**By: Daulton Moro**AAS Theorem Summary:**• The AAS theorem is one of the theorems that is used to prove triangles congruent. • The AAS theorem is when two angles and one non-included side are congruent.**Sample Problems**• For the first picture you would mark lines BC and CE congruent and angles A and D would be congruent. After mark the vertical angles congruent the you have congruence by AAS. • The second picture shows AAS because there are two angles that are congruent and one side that is non-included. • The third picture is self explanatory and is proven by using AAS.**Helpful Websites**• www.mathwarehouse.com • www.library.thinkquest.org • www.phschool.com**What exactly is an HL proof? By Dylan Sen**• The hypotenuse leg theorem, or HL, is the congruence theorem used to prove only right triangles congruent. • Also The theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.. • The goal of today’s lesson is to prove right triangles congruent using the HL theorem**Rules and Formulas**• As seen in the previous slide, if the hypotenuse and leg of one triangle are congruent to the hypotenuse and leg of the other, the triangles are congruent. • The most important formula to remember is:**Examples**Given: Prove: Statement Reason (leg)-Given (hypotenuse) - Given and -They both have a right angle. are right triangles - Through the HL theorem. Since the hypotenuse and the leg are congruent, that means the triangles are congruent**Given-**and Prove: (leg) Given (hypotenuse) Given and They have a right angle are right triangles Because the hypotenuse and corresponding leg are congruent, the triangles are congruent**Given:**and Prove Statement Reason (leg) Given (hypotenuse) Given and They have a right angle are right triangles Because the hypotenuse and corresponding leg are congruent, the triangles are congruent**Useful Websites to help you further understand HL:**• http://delta.classwell.com/ebooks/navigateBook.clg?sectionType=unit&navigation=1&prevNext=0&curSeq=235&curDispPage=239&xpqData=%2Fcontent%5B%40id%3D%27mcd_ma_geo_lsn_0395937779_p236.xml%27%5D - This is the textbook definition. It will show examples and a step by step method of figuring out how to use HL. • http://www.mathwarehouse.com/geometry/congruent_triangles/hypotenuse-leg-theorem.php - Much like the textbook, this website shows great examples and will help clarify anything you have trouble with. • http://www.onlinemathlearning.com/hypotenuse-leg.html - this example shows more guided examples, which will further help you understand the HL Theorem**Medians and CentroidsSummary: A median is a segment that**connects the vertex of a triangle to the midpoint of the opposite side. The point of concurrency (intersection) of the medians is called the centroid.Goals: The goals of this presentation are to: 1) Review Medians and Centroids2) Review Sample Problems**Medians and Centroids**• A median is a segment that connects the vertex of a triangle to the midpoint of the opposite side • The point of concurrency (intersection) of the medians is called the centroid • The distance from the vertex to the centroid is 2/3 of the total distance of the median • No matter what type of triangle (right, acute, obtuse), the centroid is ALWAYS inside the triangle**Sample Problems**1) Always, Sometimes, Never: The centroid ________________ lies within the triangle. 2) Find x: 3) Fill In The Blank: A triangle has ____________ medians.**Helpful Links**• http://www.mathopenref.com/trianglemedians.html • http://mathworld.wolfram.com/TriangleMedian.html • http://www.analyzemath.com/Geometry/MediansTriangle/MediansTriangle.html • http://www.cut-the-knot.org/triangle/medians.shtml