CK12 - Geometry

Thereis only one fold line that dividesthe triangleinto congruenttriangles,the line that foldsthe angle formedby the congruents ...

Mediansin Triangles LearningObjectives Constructthe mediansof a triangle. Applythe Concurrencyof MediansTheoremto identifythe p ...

hintsfor developingthe proof. Example1. Use The Concurrencyof MediansTheoremto find the lengthsof the indicatedsegmentsin the fo ...

Onceyou havehiddenthe circles,you will havean equilateraltriangle.You can use the constructionany time you needto constructan eq ...

Find the centroidof eachequilateraltriangleand connectthe centroidsto get the Napoleonoutertriangle. Measurethe sidesof the new ...

Drawa triangleon a sheetof card stockpaper(or thin cardboard)and locatethe centroid. Carefullycut out the triangle. Hold your p ...

Find the coordinatesof the centroid of with vertices and. Also, find. Use the examplesketchof Napoleon’s Theoremto form the f ...

You havebeenaskedto designa triangularmetallogo for a club at school.Usingthe followingrectangular coordinates,determinethe log ...

4. 5. a. b.. a. The triangleis equilateral. b. The differencein the areasof the innerand outertrianglesis equalto the area o ...

8. a. Notethat the midpointof side is locatedat the origin.Constructthe medianfrom vertex to the origin,and call it. The pointof ...

Applythe Concurrencyof AltitudesTheoremto identifythe pointof concurrencyof the altitudesof the triangle(the orthocenter). Use ...

As was true with perpendicularbisectors(whichintersectat the circumcenter),and anglebisectors(which intersectat the incenter),an ...

Evenwith thesethreecases,we may still encounterspecialtrianglesthat exhibitinterestingproperties. Example 1 Use a pieceof PattyP ...

copiesof onto PattyPaper(so that you end up with four sheetsof paper, eachshowing ). For one of the sheets,fold the paperto loc ...

Do you thinkthat the four pointswill be collinearfor all otherkindsof triangles?The answeris prettyinter- esting!In our homework ...

Prove:. Considerisoscelestriangle with , and ,. Prove:. Answers All four pointsare the same. The four pointsall lie inside ...

The proofcan be completedby usingthe AAS postulateto showthat triangles and are congruent.The conclusionfollowsfrom CPCTC. Ine ...

Since is isosceles,we have. By angleaddition,we have. So , and by substitution. Notethat is exteriorto , so. Hence, and , we ha ...

If , then by the fact that the longerside is oppositethe largest angle(the theoremwe just proved).But this too contradictsour g ...

Supposethat is the longestside.Thenstatements2 and 3 aboveare true. In orderto prove1. , constructthe perpendicularfrom point to ...