Question

Use the converse of the Pythagorean theorem to decide if the triangles are right, acute or obtuse. Then classify them.

(show work) pls help!!!!!! i’m confused

Answer 1

`\mathrm{a\ right\ triangle}`

Explanation:

`\mathrm{The\ converse\ of\ pythagoras\ theorem\ states\ that\ if\ }c^2=a^2+b^2\ \mathrm{then\ it\ is}\\\mathrm{a\ right\ angled\ triangle.\ We\ can\ therefore\ use\ the\ converse\ to\ check\ if\ a}\\\mathrm{triangle\ is\ right\ angled\ or\ not.}\\\mathrm{Here\ in\ the\ question\ we\ are\ given\ a\ triangle\ with\ 3\ sides.\ Let's\ take\ the }\\\mathrm{longest\ one\ has\ hypotenuse.\ So,\ let\ c=√(50),\ a=5\ and\ b=5.}\\`

`\mathrm{Finally,\ we\ want\ to\ test\ whether\ the\ given\ triangle\ is\ right\ angled\ or\ not\ }\\\mathrm{i.e.\ is\ }c^2=a^2+b^2?\\c^2=√(50)^2=50.\\a^2+b^2=5^2+5^2=25+25=50\\\mathrm{Here,\ the\ pythagoras\ theorem\ }c^2=a^2+b^2\ \mathrm{is\ satisfied\ so\ the\ triangle\ is}\\\mathrm{right\ angled\ triangle.}`

I hope this clarifies your doubt!