Question 1: It is given that BC = EC and AC = DC. According to the definition of vertical angles, ∠BCA = ∠DCE. Thus, the two triangles are congruent by SAS. According to CPCTC, BA must be congruent to ED.
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Question 2: A and E are base angles. B and D are legs. F is the base. C is the vertex angle.
The number of meals that students eat is a numeric variable, which makes it a quantitative variable. However, it can only be measured in integers (assuming that there is no such thing as half a meal), which makes the data he is working with a discrete quantitative variable.