TRIUNGHIUL ISOSCEL ABC CU UNGHIUL BAC=100 ARE CE SI AD BISECTOARE CU E APART.LUI AB ,IAR D APAR LUI BC,CE INTERSECTEAZA AD IN PUNCTUL F.DACA BISECTOAREA UNGHIULUI BEC INTERSECTEAZA BC IN G SA SE DEMONSTREZE CA :
a) triunghiul CAE CONGRUENT TRIUNGHIUL CGE
b)GF ESTE BISECTOAREA UNGHIULUI EGD
a)…
![Rendered by QuickLaTeX.com \rm{ daca \Delta{ABC}- isoscel si m(\hat{A})=100^0\\ \Rightarrow m(\hat{C})=m(\hat{B})=(180^0-100^0):2=40^0\\ deci \hat{ACE}=\hat{BCE}=20^0 de unde\\ \Rightarrow \hat{AEC}=60^0 adica \hat{BEC}=120^0 \\ \Rightarrow \hat{BEG}=\hat{CEG}=120^0:2=60^0\\ avem deci \{\hat{ACE}=\hat{BCE}\\ \hat{AEC}=\hat{CEG} si\\ EC\eq{EC}](https://anidescoala.ro/wp-content/ql-cache/quicklatex.com-23acbd902c93d966a8e5e0205a6cc877_l3.png)
![Rendered by QuickLaTeX.com \rm{ U.L.U \Rightarrow \Delta{CAE}\eq\Delta{CGE}.](https://anidescoala.ro/wp-content/ql-cache/quicklatex.com-447bc88f7f65dfc964a301e7316f855e_l3.png)