Transcript Geometry
Geometry 5.4 Special Parallelograms Set Up a Flow Chart to Fill in as We Go Rectangle A quadrilateral with four right angles. Why is a rectangle a parallelogram? Both Pairs of Opp. Angles are Congruent Rhombus A quadrilateral with four congruent sides. Why is a rhombus a parallelogram? Both Pairs of Opp. Sides are Congruent Square (Rhom-tangle Ha! Ha!) A quadrilateral with four congruent sides and four right angles. Why is a rhombus a parallelogram? Both Pairs of Opp. Sides are Congruent Both Pairs of Opp. Angles are Congruent 1) 2) 3) 4) Review: Rectangles, Rhombuses, and Squares all Share these Properties of a Parallelogram… Opp. Sides are // Opp. Angles are congruent Opp. Sides are congruent Diagonals Bisect Each Other In addition, rectangles, rhombuses, and squares all have their own special properties. These are the focus of this lesson. Theorem: The diagonals of a Rectangle are Congruent Draw two congruent intersecting lines that bisect each other. Connect the corners. You drew a rectangle. Theorem: The diagonals of a rhombus are perpendicular. Draw two lines that bisect each other & are perpendicular. Connect the corners. You have drawn a rhombus. Theorem: Each diagonal of a rhombus bisects two angles of the rhombus. Draw a rhombus and its diagonals. You bisected all four angles. Theorem: The midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. Draw a right triangle and put a point at the midpoint of the hypotenuse. Draw a line from that point to the vertex of the right angle. All three distances are equal. . Theorem: If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle. Draw one right angle. Draw the two other sides parallel to the opposite side. You have drawn a rectangle. Why is it a rectangle? Opp. Angles of a Parallelogram Are congruent Parallel lines imply SS Int. angles are supplementary. Theorem: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. Draw two congruent sides of an angle. Draw the two other sides parallel to the opposite sides. You have drawn a rhombus. Why is it a rhombus? Opp. Sides of a Parallelogram are congruent. Given Quad. WXYZ is a rectangle. Complete the statements with numbers. Make sure your + and – are clear! 3. If TX = 4.5, then WY = _____. W X T Z Y 4. If WY = 3a + 16 and ZX = 5a – 18, then a = _____, WY = _____ and ZX = _____. 5. If m<TWZ = 70, then m<TZW = _____ and m<WTZ = _____. Given Quad. ABCD is a rhombus. Complete the statements with numbers. 7. If m<4 = 25, then m<5 = _____. A B 4 2 1 5 8. If m<DAB = 130, then m<ADC = _____. 3 9. If m<4 = 3x – 2 and m<5 = 2x + 7, then x = ____, m<4 = ____, and m<5 =____. D C 11. If m<2 = 3y + 9 and m<4 = 2y – 4, then y = _____, m<2 = _____, and m<4 = ____. Given Quad. JKLM is a square. Complete the statements with numbers. M L M L x 14. If JL =18, then MK = _____, JX = _____, and XK = _____. X J J K K 15. m<MJK = _____, m<MXJ = _____ and m<KLJ = _____. HW P. 186 (1-11) P. 187 (1-10) (11-27 Odd) If you forget the theorems, it helps to draw a picture…i.e. draw a rhombus and then its diagonals and see if they are congruent or pependicular. A HW Jumpstart P. 187 # 5-8 Property Parallelogram Rectangle Rhombus Square 5) Diags. Bisect each other X X X X 6) Diags. Are conguent X X 7) Diags. Are Perpendicular X X 8) A diagonal Bisects 2 angles X X