Solution:
The pictureshowsus similarright triangles:the personand his shadoware the legs of one triangle,and the
tree and its shadowform the legs of the largertriangle.The trianglesare similarbecauseof their angles:
they both havea right angle,and they shareone angle.Thereforethe third anglesare also congruent,and
the trianglesare similar.
The ratio of the triangles’lengthsis 3:1. If we lethrepresentthe heightof the tree, we have:
LessonSummary
In this lessonwe havereviewedkey aspectsof triangles,includingthe namesof differenttypesof triangles,
the triangleanglesum,and criteriafor similartriangles.In the last example,we usedsimilartrianglesto
solvea probleminvolvingan unknownheight.In general,trianglesare usefulfor solvingsuchproblems,but
noticethat we did not use the anglesof the trianglesto solvethis problem.This techniquewill be the focus
of problemsyou will solvelater in the chapter.
Pointsto Consider
- Why is it impossiblefor a triangleto havemorethan one right angle?
- Why is it impossiblefor a triangleto havemorethan one obtuseangle?
- How big can the measureof an angleget?
ReviewQuestions
- TriangleABC is an isoscelestriangle.If side AB is 5 incheslong,and side BC is 7 incheslong,how long
is side AC? - Can a right trianglebe an obtusetriangle?Explain.
- A trianglehas one anglethat measures 48 oand a secondanglethat measures 28 o. Whatis the measure
of the third anglein the triangle? - Claim:the two non-rightanglesin any right triangleare complements.
a. Explainwhy this claimis true