math with mrs. solomon - welcome to math with mrs ......geometry kite: parallelogram: isosceles...

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Lesson 7-9 Notes Diagonals of Quadrilaterals Geometry Kite: Parallelogram: Isosceles Trapezoid: D c s Dayna 16 a re DI ascoa16 bisecf Ore perpend cwl CCF. eacV'l C\her. Djoqona16 co c o are NOT cc Rectangle: C S are perperdtccdQF. b16ec+ each c+ber \ \s€cå each and DiQYQlB are Dja coa\6 are 04bé bi C Rc± +e Square: C a perpendicecfar DIO cue 0 4

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Page 1: Math with Mrs. Solomon - Welcome to Math with Mrs ......Geometry Kite: Parallelogram: Isosceles Trapezoid: D c s Dayna 16 a re DI ascoa16 bisecf perpend cwl CCF. eacV'l C\her. Djoqona16

Lesson 7-9 Notes

Diagonals of Quadrilaterals

Geometry

Kite: Parallelogram: Isosceles Trapezoid:

D c

s

Dayna 16 a re DI ascoa16 bisecfOreperpend cwl CCF. eacV'l C\her. Djoqona16

co co are NOT cc

Rectangle:

CS

are perperdtccdQF.

b16ec+ each c+ber \ \s€cå each

andDiQYQlB are

Dja coa\6 are04bé biCRc± +e

Square:C

a perpendicecfar DIOcue 0 4

Page 2: Math with Mrs. Solomon - Welcome to Math with Mrs ......Geometry Kite: Parallelogram: Isosceles Trapezoid: D c s Dayna 16 a re DI ascoa16 bisecf perpend cwl CCF. eacV'l C\her. Djoqona16

Back to Lesson 7-9

Name

Lesson Master

Objective B

Answer Page

Questions on SPUR ObjectivesSee Student Edition pages 445—449 for objectives.

In 1—3, name all of the special quadrilaterals that exhibit the property.

1. The diagonals are congruent.

2. The diagonals are both congruent and perpendicular.

3. The diagonals are perpendicular but not necessarily congruent.

Objective F

In 4—6 give the most specific name uadrilateral.

4. 6.

Square s oscees

Objective H

7. The Park District wants to make paths through Woodruff Park,

which is a parallelogram formed by 4 streets. If they make the

paths the diagonals of the parallelogram, the paths will meet at

right angles. What can you conclude about the lengths of the

Auburn Ave.

streets bordering the park?

Edgewood Ave.

REPRESENTATIONS Objective J

8. Arrange isosceles trapezoid, kite, parallelogram,

rectangle, rhombus, and square in a hierarchy

based on diagonals being perpendicular bisectors,

congruent, and/or bisectors of each other.

9. A quadrilateral has diagonals that are perpendicular

but not congruent. What kind of figure could it be?

kiR (Y

302 Geometry

Page 3: Math with Mrs. Solomon - Welcome to Math with Mrs ......Geometry Kite: Parallelogram: Isosceles Trapezoid: D c s Dayna 16 a re DI ascoa16 bisecf perpend cwl CCF. eacV'l C\her. Djoqona16

Back to Lesson 7-9

Name

Lesson Master

Objective B

Answer Page

Questions on SPUR ObjectivesSee Student Edition pages 445—449 for objectives.

In 1—3, tell all you can about the diagonals of the figure.

1. ectangle RECT

•aoa'.Pta onC115 bisec+ each

c

2. trapezoid TRAP

bc Iso€e\es KnowSin€cfvmcuhon wbocc+ cliocyvnæb

3. figureABCD - liEele6 hopez-0id

nais con

In 4 and 5, mark all pairs of congruent segments and angles in the figure.

PQRS is a rectangle. 5 EFGHis a parallelogram.

H

PROPERTIES Objective F

6. What must be true about the diagonals of this figure for it to be a square?O

7. What must be true about the diagonals of this figure for it to be a rectangle?

-O

Geometry 303

Page 4: Math with Mrs. Solomon - Welcome to Math with Mrs ......Geometry Kite: Parallelogram: Isosceles Trapezoid: D c s Dayna 16 a re DI ascoa16 bisecf perpend cwl CCF. eacV'l C\her. Djoqona16

Back to Lesson 7-9

Name

7-9B

Objective H

8. An expandable gate is constructed so that for each quadrilateral region,AB = CD and AD = BC for any position of the gate. The picture shows asquare gate. Explain why AB and BC are perpendicular.

Abl

0

In 9—13, use the hierarchy of quadrilaterals one diagonal is theat the right to name all possible figures. perpendicular bisector

of the other.

9. If both parts of the diagonals of aquadrilateral are congruent, and onediagonal is the perpendicular bisectorof the other, the figure is a

10. If one diagonal of a quadrilateral is theperpendicular bisector of the otherdiagonal, the figure is a

11. If the diagonals of a quadrilateral are

kite

rhombus

Diagonals bisecteach other.

parallelogram

square

perpendicular bisectors of each other,the figure is a

12. If the diagonals of a quadrilateral bisect each other, the figure is a

13. If the diagonals of a quadrilateral bisect each other and both parts of

Answer Pac

page 2

Both parts ofdiagonals arecongruent.

isosceles trapezoid

rectangle

o

them are congruent, e figure is a

304 Geometry