IM Geo.2.13 Practice: Proofs about Parallelograms

Conjecture:

A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.

Restate the conjecture as a specific statement using the diagram.

is congruent to , and is parallel to . Show that is a parallelogram.

Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles trapezoid are congruent.

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A
In parallelogram , show triangle is congruent to triangle .
B
In parallelogram , show triangle is congruent to triangle .
C
In parallelogram , show is congruent to and is congruent to .
D
In quadrilateral with congruent to and congruent to , show is a parallelogram.

Is triangle congruent to triangle ? Explain your reasoning.

Select all true statements based on the diagram.

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Which conjecture is possible to prove?

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A
If the four angles in a quadrilateral are congruent to the four angles in another quadrilateral, then the two quadrilaterals are congruent.
B
If the four sides in a quadrilateral are congruent to the four sides in another quadrilateral, then the two quadrilaterals are congruent.
C
If the three angles in a triangle are congruent to the three angles in another triangle, then the two triangles are congruent.
D
If the three sides in a triangle are congruent to the three sides in another triangle, then the two triangles are congruent.