1 (Dolce & Pompeu-adapted) Check the options that are true.
2-In the figure below, the triangles ABC and CDA are congruent. Calculate the value of x and y.[br][br][br][br] [img]data:image/png;base64,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[/img]
Knowing that the triangle ABC below has an isosceles base BC, calculate the value of x.[br] [img]data:image/png;base64,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[/img][br]The solution steps are described in the following items. Explain each one.
a) Note that [math]\ \hat{B}=\hat{C}=70º [/math]. Therefore, BP is an angle bisector of [math]\ \hat{B}[/math].[br]
b) In the triangle BPC, we have [math]\ C\hat{B}P[/math]=35º and [math]\ B\hat{C}P[/math]=55º. So [math]\ \hat{P}[/math]=90º.
c) In the triangle CBE, BP is an angle bisector and also the height. So the triangle CBE has an isosceles base on CE. Therefore, P is the midpoint of EC.
d) Now, considering the DEC triangle, where DP is median and height, we conclude that this triangle has an isosceles base EC. So, we have [math]\ C\hat{E}D[/math]=15º and x=75º.