Geometry Unit 6 Note Sheets Date Name of Lesson. 6.2 Parallelograms. 6.3 Tests for Parallelograms. 6.4 Rectangles. 6.5 Rhombi and Squares
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1 Date Name of Lesson 6.2 Parallelograms 6.3 Tests for Parallelograms 6.4 Rectangles 6.5 Rhombi and Squares 6.6 Trapezoids and Kites 1
2 Quadrilaterals Properties Property Parallelogram Rectangle Rhombus Square Quadrilateral Trapezoid Isosceles Trapezoid Both pairs of opp sides are Exactly 1 pair of opp sides are A A A A S N N N N N N N S A A N Diagonals are ^ S S A A S S S A Diagonals S A S A S A A S Kite Diagonals bisect each other Interior Angles add up to 360 degrees. Both pairs of opp sides All sides Both pairs of opp angles Exactly 1 pair of opp angles All angles All Ð Base Ð A A A A S S S S A A A A A A A A A A A A S S S N S S A A S S S S A A A A S S S S N N N N S S S A A A S A S S S S A A S A S S S S n/a n/a n/a n/a A S A n/a A Always N Never S Sometimes n/a not applicable 2
3 6.2 Parallelograms Notes Parallelogram Properties of Parallelograms 4
4 Find the value of each variable in the parallelogram
5 7. Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices!( 2, 4), ((3, 5), +(2, 3), and,( 3, 4). Steps: 1. Name the diagonals. 2. Find the midpoint of the diagonals. 8. Determine the coordinates of the intersection of the diagonals of parallelogram RSTU with vertices -( 8, 2), /( 6, 7), 2(6, 7), and 3(4, 2). Steps: 1. Name the diagonals. 2. Find the midpoint of the diagonals. 9. 6
6 6.3 Tests for Parallelograms Notes Conditions for Parallelograms Determine whether the quadrilateral is a parallelogram. Justify your answer
7 5. If!4 = 36 1, 4( = ,,4 = 68 2, and 4+ = , find 6 and 8 so that the quadrilateral is a parallelogram. 6. Find 6 and 8 so that the quadrilateral is a parallelogram. Graph each quadrilateral with the given vertices. Determine whether the figure is a parallelogram. Justify your answer , 3, : 8, 4, ;(7, 2), and <(1, 3) Steps: 1. Find the distance of each side. 2. Find the slopes of sides. 8
8 8. =( 1, 3), -(3, 1), /(2, 3), and 2( 2, 1) Steps: 1. Find the midpoint of the diagonals. 2. Find the slopes of sides. 9. A student is given the following information and then asked to write a paragraph proof. Determine which statement would correctly complete the student s proof. Given: Parallelogram >-/2 and Parallelogram >=?3 Prove:? / Proof: We are given Parallelogram >-/2 and Parallelogram >=?3. Since opposite angles of a parallelogram are congruent, >? and > /.. A. Therefore,? / by the Transitive Property of Congruence. B. Therefore,? / by the Transformative Property of Congruence. C. Therefore,? / by the Reflective Property of Congruence. D. Therefore,? / by the Reflexive Property of Congruence. 9
9 6.4 Rectangles Notes Rectangle Properties of Rectangles Diagonals of a Rectangle A rectangular park has two walking paths as shown. 1. If >/ = 180 DEFEGH and >- = 200 DEFEGH, find =2. 2. If D >-/ = 64, find D /=-. 3. Using the rectangular park, if 2/ = 120 DEFEGH find >-. 10
10 4. Quadrilateral,4:; is a rectangle. If D 4,: = and D,:4 = , find Quadrilateral -/23 is a rectangle. If D -23 = and D /3- = 36 2, find Quadrilateral >=-/ has verticies >( 5, 3), =(1, 1), -( 1, 4), and /( 7, 0). Determine whether >=-/ is a rectangle. Find the area. Steps: 1. Find the distance of each side. 2. Find the distance of the diagonals. 3. Find the area. 11
11 7. Quadrilateral,4:; has verticies,( 2, 3), 4(1, 4), :(3, 2), and ;(0, 3). Determine whether,4:; is a rectangle. Steps: 1. Find the slopes. 8. What is the value of x in the rectangle? 9. What is the value of x in the rectangle? 12
12 6.5 Rhombi and Squares Notes Rhombus Square Diagonals of a Rhombus The diagonals of rhombus!(+, intersect at 4. Use the given information to find the each measure or value. 1. If D!,+ = 82, find D 4+,. 2. If (+ = and,+ = 56 2, find 6. The diagonals of rhombus KLMN intersect at?. Use the given information to find the each measure or value. 3. If D KNL = 39.5, find D NML. 4. If KL = 86 5 and KN = , find 6. 13
13 5.,4:; is a rhombus. If D,;: = 84 and D,4; = ( ), find the value of 6. 6.,4:; is a rhombus. If D,;: = 100 and D,4; = ( ), find the value of 6. 14
14 Conditions for Rhombi and Squares 5. Determine whether parallelogram JKLM with vertices,( 7, 2), 4(0, 4), :(9, 2), and ;(2, 4) is a rhombus, a rectangle, or a square. List all that apply. Explain (Remember to find distances, slopes, midpoints to help explain.) 6. Determine whether parallelogram ABCD with vertices P( 2, 1), Q( 1, 3), R(3, 2), and S(2, 2) is a rhombus, a rectangle, or a square. List all that apply. Explain 15
15 6.6 Trapezoids and Kites Notes Trapezoid Isosceles Trapezoid Isosceles Trapezoids The speaker shown is an isosceles trapezoid. If D!,+ = 85,!4 = 8 TUVhEH, and,( = 19 TUVhEH, find each measure. 1. D!( Each side of the basket shown is an isosceles trapezoid. If D,;: = 130, 4< = 6.7 XEEF, and ;< = 3.6 XEEF, find each measure. 3. D ;,4 4.,: 16
16 5. Quadrilateral ABCD has vertices P( 3, 4), Q(2, 5), R(3, 3), and S( 1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 6. Quadrilateral ABCD has vertices P(5, 1), Q( 3, 1), R( 2, 3), and S(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 17
17 midsegment of a trapezoid Trapezoid Midsegment Theorem 7. In the figure :+ is the midsegment of trapezoid!(,4. What is the value of x? 8. In the figure ;< is the midsegment of trapezoid!(,4. What is the value of x? 18
18 Kite Kites 9. If!(+, is a kite, find D (!,. 10. If KLMN is a kite, find NM. 11. If KLMN is a kite, find D LMN. 12. If ;<>= is a kite, find <>. 19
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