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Lesson 7-9 Notes
Diagonals of Quadrilaterals
Geometry
Kite: Parallelogram: Isosceles Trapezoid:
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s
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co co are NOT cc
Rectangle:
CS
are perperdtccdQF.
b16ec+ each c+ber \ \s€cå each
andDiQYQlB are
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Square:C
a perpendicecfar DIOcue 0 4
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
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
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