Unit 2, Lesson 13
Proofs about Parallelograms
Geometry
Practice
Problem 2
In quadrilateral \(ABCD\), \(AD\) is congruent to \(BC\), and \(AD\) is parallel to \(BC\). Show that \(ABCD\) is a parallelogram.
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In quadrilateral \(ABCD\), \(AD\) is congruent to \(BC\), and \(AD\) is parallel to \(BC\). Show that \(ABCD\) is a parallelogram.
\(ABDE\) is an isosceles trapezoid. Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles trapezoid are congruent.
Select the conjecture with the rephrased statement of proof to show that the diagonals of a parallelogram bisect each other.
In parallelogram \(EFGH\), show triangle \(HEF\) is congruent to triangle \(FGH\).
In parallelogram \(EFGH\), show triangle \(EKH\) is congruent to triangle \(GKF\).
In parallelogram \(EFGH\), show \(EK\) is congruent to \(KG\) and \(FK\) is congruent to \(KH\).
In quadrilateral \(EFGH\) with \(GH\) congruent to \(FE\) and \(EH\) congruent to \(FG\), show \(EFGH\) is a parallelogram.
Is triangle \(EJH\) congruent to triangle \(EIH\)?
Explain your reasoning.
\(\overline{HJ} \perp \overline{JE}, \overline{HI} \perp \overline{IE}, \overline{HJ} \cong \overline{HI}\)
Select all true statements based on the diagram.
Segment \(DC\) is congruent to segment \(AB\).
Segment \(DA\) is congruent to segment \(CB\).
Line \(DC\) is parallel to line \(AB\).
Line \(DA\) is parallel to line \(CB\).
Angle \(CBE\) is congruent to angle \(DEA\).
Angle \(CEB\) is congruent to angle \(DEA\).