Please help with Issacs Exercises ID: #'s 3, 7, 9 *, 11

*NOTE: There is a typo in the hint; replace ?C with ?B.

For Exercises 1D, you can use the latter (as we proved it in 1C), but do not use the Pythagorean Theorem.

ID PARALLELOGRAMS 17 Exercises ID 1D.1 Prove Theorem 1.7 by showing that quadrilateral ABCD is a parallelogram if AB = CD and AD = BC. 1D.2 Prove Theorem 1.8 by showing that quadrilateral ABCD is a parallelogram if AB = CD and ABI|CD. 1D.3 Prove that the diagonals of a rectangle are equal. 1D.4 Prove that a parallelogram having perpendicular diagonals is a rhombus. 1D.5 Prove that a parallelogram with equal diagonals is a rectangle. 1D.6 In Figure 1.15, we are given that ABI|CD and that AD and BC are not parallel. Show that LD = LC if and only if AD = BC. HINT: Draw a line through B parallel to AD. Figure 1.15 NOTE: Recall that a quadrilateral is said to be a trapezoid if it has exactly one pair of parallel sides. If the nonparallel pair of sides are equal, the trapezoid is said to be isosceles. 1D.7 Show that opposite angles of a parallelogram are equal. 1D.8 In quadrilateral ABCD, suppose that A BI|CD and LB = LD. Show that ABCD is a parallelogram. 1D.9 In quadrilateral ABCD, suppose that LA = LC and LB = LD. (We are referring to the interior angles, of course.) Show that ABCD is a parallelogram. HINT: Show that LA and LC are supplementary. 1D.10 Show that the diagonals of an isosceles trapezoid are equal. 1D.11 In Figure 1.16, we are given that AAXB and AAY B are isosceles and share base AB. Show that points X, Y, and Z are collinear (lie on a common line) if and only if AAZB is isosceles with base AB. B Figure 1.16