Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name:_____________________________ Unit 4: Properties of Polygons 4.1 Parallelograms 4.2 Rectangles 4.3 Squares/ Rhombi 4.4 Trapezoids and Kites 4.5 2-Column Proofs GEOMETRY Unit 4, Quadrilaterals Notes 4-1, Parallelograms Parallelograms Name ________________________ Date __________ Period _________ (Note: All quadrilaterals in this set of notes are parallelograms.) A parallelogram is a quadrilateral with both pairs of opposite sides parallel. (Mark the parallel sides of parallelogram ABCD) Draw a picture to illustrate your conjecture Parallelogram Conjecture #1 (6-1) : Opposite sides of a parallelogram are __________________ Ex 1: Solve for x and y. Ex 2: Solve for x and y. Ex 3: Solve for x and find AB. Draw a picture to illustrate your conjecture Parallelogram Conjecture #2 (6-2) Opposite angles of a parallelogram are ______________. Ex 4: Solve for x and y. Ex 5: Solve for x Ex 6: Solve for x and y & find m D . & find m C and m D . 2 ˚ ˚ ˚ ˚ ˚ Draw a picture to illustrate your conjecture Parallelogram Conjecture #3 (6-3): Consecutive angles of a parallelogram are _______________. Ex 7: If mA 115 , find mB , mC and mD . Ex 8: Solve for x and find mC . ˚ ˚ Ex 9: Find mA and mD . 3 Parallelogram Conjecture #4 (6-4): The diagonals of a parallelogram ____________________ Ex 10: If AE = 8, find EC. Ex 11: If EB = 12 and DE = 3x, solve for x. Ex 12: If DE = 7x + 2 and EB = 9x – 6, find DB. Ex 13: If EC = 3x – 8 and AC = 4x +6, solve for x and find AC. Ex 14: Solve for x. Ex 15: Solve for x and y. ˚ ˚ GEOMETRY Unit 4, Quadrilaterals ˚ 4 Notes 4-2, Rectangles Rectangles Name ________________________ Date __________ Period _________ Determine if the quadrilateral with the given vertices is a parallelogram. R (1, 1), S (3, 6), T (9, 8) and V (7, 3) Definition of a rectangle - Determine if the quadrilateral with the given vertices is a rectangle. R (2, 2), S (0, 6), T (6, 9) and V (8, 5) Note that a rectangle is a special type of __________________________. Therefore, a rectangle has the following properties: 5 Property Why does it have this property? 1. 2. 3. 4. 5. Rectangle Conjecture #1 (6-9): Use rectangle ABCD to answer the following (treat each question independently): 1. If EB = 12, then AE = _______ 2. If EC = 12x – 4 and DE = 44, then x = _______ 3. If AE = 5x – 2 and DB = 6x + 16, then AC = _______ 4. If mEAD 49 , then mAED = ______ and mAEB = _______ Use rectangle ABCD to answer the following questions: 5. If m1 43 and m3 13x 4 , then x = _______ 6 6. If m4 7 x 5 and m6 5x 13 , then m4 = _______ and m5 = _______ 7. If m7 2x 7 and m10 6x 10 , then m7 = _______ 8. If m4 9x 5 and m8 7 x 1 , then m8 = _______ 7 GEOMETRY Unit 4, Quadrilaterals Notes 4-3, Squares and Rhombi Squares and Rhombi Name ________________________ Date __________ Period _________ Definition of a rhombus - Rhombus Conjecture #1 (6-11): The diagonals of a rhombus are ______________________. Rhombus Conjecture #2 (6-13): Each diagonal of a rhombus _______________________________. Ex 1: Use rhombus ABCD to answer the following questions. (Treat each problem independently.) (a) If AB = 7x + 3 and DC = 10x – 6, then AD = _______ (b) If AC = 32, then EC = _______ (c) If m1 2x 20 and m2 5x 4 , then x = ________ (d) If m7 5x 2 and m8 3x 10 , then m8 = _______ (e) If m5 51 , then mABC = _______ and mBCD = _______ (f) If m2 58 , then m3 = ________ Definition of a square - 8 Ex 2: Use square ABCD to answer the following questions. (Treat each problem independently.) (a) If AB = 2x + 3 and BC = 3x – 5, then DC = ________ (b) Find m8 _______ (c) If DB = 5x – 2 and EB = 2x + 4, then DB = _______ and AE = ________ Property Parallelogram Rectangle Rhombus Square The diagonals bisect each other. The diagonals are congruent. Each diagonal bisects a pair of opposite angles. The diagonals are perpendicular Opposite angles are congruent. All four angles are right angles. All four sides are congruent. 9 GEOMETRY Unit 4, Quadrilaterals Notes 4-4, Trapezoids and Kites Name ________________________ Date __________ Period _________ Trapezoids and Kites Definition of a trapezoid - If the legs of a trapezoid are congruent, then Isosceles Trapezoid Theorem #1 (6-14) Isosceles Trapezoid Theorem #2 (6-15) Use isosceles trapezoid ABCD above to answer the following questions: Ex 1: If mABC 116 , then mDAB = ______, mADC = ______, mDCB = ______ Ex 2: If AC = 8x – 1 and BD = 6x + 9, then AC = ______ 10 The median of a trapezoid is Trapezoid Median Theorem Use trapezoid ABCD below, where EF is a median, to answer the following questions: Ex 3: AB = 6 and DC = 14, then EF = _______ Ex 4: If AB = 2x – 6, DC =3x – 3 and EF = 13, then x = ______ Ex 5: If mADC 43 , then mAEF = _______ Ex 6: If AE = 6, then AD = _______ Ex 7: If BF = 3x + 2 and FC = 5x – 4, then BF = ______ and BC = ______ A kite is a quadrilateral with two pairs of adjacent congruent sides. Label the congruent sides on kite ABCD. Ex 8: If AB = 3x + 1 and AD = 4x – 7, then AD = _______ 11 Use the “GG-Kites” applet on the website to come up with some conjectures about kites. Kite Conjecture #1:__________________________________________________ Kite Conjecture #2:__________________________________________________ Kite Conjecture #3:____________________________________________ 12