Proofs about Parallelograms
Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.
1) Draw a diagram of the situation and mark the given information on the diagram.
2) Restate the conjecture as a specific statement using the diagram.
3) In quadrilateral , is congruent to , and is parallel to . Show that is a parallelogram.
4) is an isosceles trapezoid. Select all of the statements that could be used to show that the diagonals of an isosceles trapezoid are congruent. Write each corresponding letter in the answer box and separate letters with commas.
a) b) c) d) e) There are none.
5) Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
6) Is triangle congruent to triangle ?
Given: , ,
7) Explain your reasoning.
8) Select all true statements based on the diagram. Write each corresponding letter in the answer box and separate letters with commas.
a) Segment is congruent to segment . b) Segment is congruent to segment . c) Line is parallel to line . d) Line is parallel to line . e) Angle is congruent to angle . f) Angle is congruent to angle .
9) Which conjecture is possible to prove?