CK12 - Geometry

Thenconnectthe midpointsof the sidesof the triangle.Shadein the centraltriangle. This is Level1. Now repeatthis processto create ...

Now let’s see how the SierpinskiTriangleis self-similar. Lookat the trianglethat is outlinedin the diagramabove.Couldyou proveth ...

How manyunshadedtrianglesare therein Leveln? Supposethe area of the Startlevel triangleis. Whatis the total area of the unsh ...

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. The midsegmentsof a triangledivideit into four congruenttriangles,eachof whichis similarto th ...

8. RightTriangleTrigonometry.................................................................................................... ...

The legs of the triangleaboveare inchesand inches.The hypotenuseis inches.So, , , and. We can substitutethesevaluesinto the form ...

Theseare all true by the trianglesimilaritypostulate. Now, usingsimilartriangles,we can set up the followingproportion: and Putt ...

operationsto solvethe equation,and alwayskeepboth sidesof the equation“balanced”. In algebrayou learnedthat because,for example, ...

is a Pythagoreantriple.You can extrapolatethat this ratio,multipliedby greaterfactors,will also yield numbersthat satisfythe Pyt ...

If you look at the smallertrianglenow inscribedin the originalshape,you’llnoticethat it is a right triangle with one leg and hyp ...

and . The questionasksyou to identifythe lengthof the segment.Becausethe segmentis not parallelto either axis,it is difficultto ...

DistanceFormula: Givepoints and , the lengthof the segmentcon- nectingthosetwo pointsis Example 6 Use the distanceformula to fin ...

Whatis the lengthof in the trianglebelow? Do the numbers , , and makea Pythagoreantriple? Whatis the distancebetween and? Whati ...

Whatis the area of the trianglebelow? An alternativeproofof the PythagoreanTheoremusesthe area of a square.The diagrambelowshow ...

no [Diff: 1] [Diff: 2] inches[Diff: 2] [Diff: 2] squaremillimeters[Diff: 3] squarefeet [Diff: 3] squareyards[Diff: 3] 11.Proof ...

Identifyacutetrianglesfrom side measures. Identifyobtusetrianglesfrom side measures. Classifytrianglesin a numberof differentwa ...

of the PythagoreanTheoremstatesthat if , then the triangleis a right triangle. IdentifyingAcuteTriangles Usingthe converseof the ...

obtuse.You can solvethis problemin a manneralmostidenticalto example2 above. Example 3 Is the trianglebelowacuteor obtuse? The t ...

The two shortersidesof the triangleare and. The longestside of the triangleis. First find the sum of the squaresof the two short ...

The squareof the longestside is Sincethesetwo valuesare equal, , and this is a right triangle. LessonSummary In this lesson,we e ...