Answers
6. Open a new sketch and construct a segment AB. Next, construct any point C (not on segment AB). Construct segment BC. Select segment BC and point A, and construct the parallel line to BC through A. Next, select segment AB and point C, and construct the parallel line to AB through C. Construct the intersection, D, of the two lines. Hide the lines, and construct segments CD and DA. Drag either points A, B or C. Does the construction pass the drag test? Use congruent triangles to prove that opposite sides in a parallelogram are congruent.
7. Construct segment AB. Next construct a circle with center at B and radius AB. Now construct a point C on the circle and construct segment BC. Hide the circle. Now construct a circle with center at C and radius BC. Construct another circle with center at A and radius AB. Find the intersection of both circles and label it D. Construct segments CD and DA. Measure the sides to convince yourself that they are congruent. Drag one of vertices A, B or C. Argue that ABCD is a rhombus.
13. Open a new sketch a construct a segment AB. Next, construct a point C (not on segment AB). Construct segment AB and point C, and construct the parallel line to AB through C. Select line AB and construct a point D on it. Hide the line and construct segments CD and DA. Quadrilateral ABCD is a trapezoid. Is a rectangle a trapezoid? Is a square a trapezoid?