Unit 1, Lesson 13
Proofs about Parallelograms
Integrated Math 2
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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.
Priya is convinced the diagonals of the isosceles trapezoid are congruent. She knows that if she can prove triangles that include the diagonals congruent, then she will show that diagonals are also congruent. Help her complete the proof.
\(ABDE\) is an isosceles trapezoid.
Draw auxiliary lines that are diagonals \(\underline{\hspace{.5in}1\hspace{.5in}}\) and \(\underline{\hspace{.5in}2\hspace{.5in}}\). \(AB \) is congruent to \(\underline{\hspace{.5in}3\hspace{.5in}}\)because they are the same segment. We know angle \(B\) and \(\underline{\hspace{.5in}4\hspace{.5in}}\) are congruent. We know \(AE\) is congruent to \(\underline{\hspace{.5in}5\hspace{.5in}}\). Therefore, triangle \(ABE \) and \(\underline{\hspace{.5in}6\hspace{.5in}}\) are congruent because of \(\underline{\hspace{.5in}7\hspace{.5in}}\). Finally, diagonal \(BE\) is congruent to \(\underline{\hspace{.5in}8\hspace{.5in}}\) because \(\underline{\hspace{.5in}9\hspace{.5in}}\).
List the side lengths in order from least to greatest.