tailieunhanh - Structure question 6

Tham khảo tài liệu 'structure question 6', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THEA MATH REVIEW Quadrilaterals A quadrilateral is a four-sided polygon. Since a quadrilateral can be divided by a diagonal into two triangles the sum of its interior angles will equal 180 180 360 degrees. 1 5 3 . - 4 2 6 2 6 3 5 4 mZ1 mZ2 mZ3 mZ4 mZ5 mZ6 360 Parallelograms A parallelogram is a quadrilateral with two pairs of parallel sides. B C C A A D In the figure above AB CD and BC AD. Parallel lines are symbolized with matching numbers of triangles or arrows. A parallelogram has opposite sides that are congruent AB CD and BC AD opposite angles that are congruent mZA mZC and mZB mZD consecutive angles that are supplementary mZA mZB 180 mZB mZC 180 mZC mZD 180 mZD mZA 180 diagonals line segments joining opposite vertices that bisect each other divide each other in half Special Types of Parallelograms A rectangle is a parallelogram that has four right angles. x EJ y y x 165 THEA MATH REVIEW A rhombus is a parallelogram that has four equal sides. x x A square is a parallelogram in which all angles are equal to 90 degrees and all sides are congruent. A square is a special case of a rectangle where all the sides are congruent. A square is also a special type of rhombus where all the angles are congruent. Diagonals of Parallelograms Rectangular ABCD AC BD Rhombus ABCD AC 1 BD Square ABCD AB 1 CD AC BD In this diagram parallelogram ABCD has diagonals AC and BD that intersect at point E. The diagonals of a parallelogram bisect each other which means that AE EC and BE ED. In addition the following properties hold true The diagonals of a rhombus are perpendicular. The diagonals of a rectangle are congruent. The diagonals of a square are both perpendicular and congruent. Example In parallelogram ABCD the diagonal AC 5x 10 and BC 9x. Determine the value of x. 166 THEA MATH REVIEW Since the diagonals of a parallelogram are congruent the lengths are equal. We can then set up and solve the equation 5x 10 9x to determine the value of x. 5x 10 9x 10 4x x Subtract x from .