CK12 - Geometry

RightIsoscelesTriangles

The first type of right triangleto examineisisosceles.As you know, isoscelestriangleshavetwo sidesthat
are the samelength.Additionally, the baseanglesof an isoscelestriangleare congruentas well.An

isoscelesrighttrianglewill alwayshave base anglesthat each measure and a vertexanglethat measures

.

Don’tforgetthat the baseanglesare the anglesacrossfrom the congruentsides.Theydon’thaveto be on
the bottomof the figure.

Becausethe anglesof all triangleswill, by definition,remainthe same,all
trianglesaresimilar,so their sideswill alwaysbe proportional.To find the relationshipbetweenthe sides,
use the PythagoreanTheorem.

Example 1

The isoscelesright trianglebelowhas legs measuring

centimeter.

Use the PythagoreanTheoremto find the lengthof the hypotenuse.

Sincethe legs are centimetereach,substitute for both and , and solvefor :