Question

ABCD este un trapez dreptunghic, masura unghiului A = masura unghiului D = 90 grade , AB paralel CD cu AB=20 cm si DC=8 cm.Daca punctul M apartine laturii {AD},astfel incat MD=6cm si AD= 16 cm,verificati daca masura unghiului MCB este de 90 grade

Answer 1

   
[tex]\text{Desenul este in fisierul atasat,}\\\\ \text{In trapezul ABCD desemnam segmentele:}\\ MC,~MB,~CP\perp AB,~P\in AB.\\\\ \text{In }\Delta BCP~\text{avem:}\\ PB=AB-CD=20-8=12~cm\\ CP=AD=16~cm\\ \Rightarrow~BC=\sqrt{PB^2+CP^2}=\sqrt{12^2+16^2}= \sqrt{144+256}= \sqrt{400}=\boxed{20cm}\\\\ \text{In }\Delta CDM~\text{avem:}\\ MD=6~cm\\ CD=8~cm\\ \Rightarrow~MC=\sqrt{MD^2+CD^2}=\sqrt{6^2+8^2}=\sqrt{36+64}= \sqrt{100}=\boxed{10~cm}\\\\ \text{In }\Delta ABM~\text{avem:}\\ AM=AD-MD=16-6=\boxed{10~cm}[/tex]


[tex]\text{In triunghiurile }\Delta MBA \text{ si }\Delta MBC \text{ avem:}\\\\ MA = MC = 10~cm\\ BA = BC = 20~cm\\ MB = \text{latura comuna}\\\\ \Longrightarrow~\text{Suntem in cazul LLL de congruenta.}\\\\ \Longrightarrow~ \Delta MBA \equiv \Delta MBC\\\\ \Longrightarrow~m(\sphericalangle MCB) = m(\sphericalangle MAB) = \boxed{90^o}[/tex]

Answer 2

Am anexat o rezolvare !
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