In isosceles ∆ABC, points M and N belong to base BC so that BM = CN. Prove: ∆AMN is an isosceles triangle.

Find the value of a. the diagram is not to scale. a quadrilateral is drawn. the upper and lower sides are parallel. the interior angle in the upper left corner is labeled a degrees. the angle in the upper right corner is labeled 113 degrees. the angle in the lower right corner is labeled b degrees. the angle in the lower left corner is labeled 36 degrees. a. 36 b. 144 c. 54 d. 126

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Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.