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41. Prove: The bisectors of any two consecutive angles of a parallelogram are perpendicular. 42. Prove Theorem 5.25: A parallelogram is a rhombus if and only if its diagonals bisect the opposite angles. 43. In parallelogram ABCD, AE bisects ZA and CF bisects ZC. Prove that AECF is a parallelogram.

41. Prove: The bisectors of any two consecutive angles of a parallelogram are perpendicular. 42. Prove Theorem 5.25: A parallelogram is a rhombus if and only if its diagonals bisect the opposite angles. 43. In parallelogram ABCD, AE bisects ZA and CF bisects ZC. Prove that AECF is a parallelogram.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Help with problems 41 & 43 please? 

PROOFS 37. Prove Theorem 5.18: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 38. Prove that the diagonals of a rhombus bisect each other. 39. Prove: If ABCD is a rhombus, then ZCAD and ZBDA are complementary. 40. Prove: In parallelogram ABCD, if 2CAD and ZBDA are complementary, then ABCD is a rhombus. 41. Prove: The bisectors of any two consecutive angles of a parallelogram are perpendicular. 42. Prove Theorem 5.25: A parallelogram is a rhombus if and only if its diagonals bisect the opposite angles. 43. In parallelogram ABCD, AE bisects LA and CF bisects ZC. Prove that AECF is a parallelogram. В E D F A
Transcribed Image Text:PROOFS 37. Prove Theorem 5.18: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 38. Prove that the diagonals of a rhombus bisect each other. 39. Prove: If ABCD is a rhombus, then ZCAD and ZBDA are complementary. 40. Prove: In parallelogram ABCD, if 2CAD and ZBDA are complementary, then ABCD is a rhombus. 41. Prove: The bisectors of any two consecutive angles of a parallelogram are perpendicular. 42. Prove Theorem 5.25: A parallelogram is a rhombus if and only if its diagonals bisect the opposite angles. 43. In parallelogram ABCD, AE bisects LA and CF bisects ZC. Prove that AECF is a parallelogram. В E D F A
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