CK12 - Geometry

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

Thereare infinitelymanyPythagoreantriples,but a few of the mostcommononesand their multiplesare:

Triple

Areaof an IsoscelesTriangle

Thereare manydifferentapplicationsof the PythagoreanTheorem.One way to use The Pythagorean
Theoremis to identifythe heightsin isoscelestrianglesso you can calculatethe area.The area of a triangle
is half of the productof its baseand its height(alsocalledaltitude).This formulais shownbelow.

If you are giventhe baseand the sidesof an isoscelestriangle,you can use the PythagoreanTheoremto
calculatethe height.Recallthat the height(altitude)of a triangleis the lengthof a segmentfrom one angle
in the triangleperpendicularto the oppositeside.In this casewe focuson the altitudeof isoscelestriangles
goingfrom the vertexangleto the base.

Example 4

Whatis the heightof the trianglebelow?

To find the area of this isoscelestriangle,you will needto knowthe heightin additionto the base.Drawin
the heightby connectingthe vertexof the trianglewith the baseat a right angle.

Sincethe triangleis isosceles,the altitudewill bisectthe base.Thatmeansthat it will divideit into two

congruent,or equalparts.So, you can identifythe lengthof one half of the baseas centimeters.