Download Reading 6.5

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LESSON
6-5
Reading Strategies
Reading a Table
Theorem
Example
If one angle of a parallelogram is a right angle, then
the parallelogram is a rectangle.
If the diagonals of a parallelogram are congruent, then
the parallelogram is a rectangle.
If one pair of consecutive sides of a parallelogram is
congruent, then the parallelogram is a rhombus.
If the diagonals of a parallelogram are perpendicular,
then the parallelogram is a rhombus.
If one diagonal of a parallelogram bisects a pair of
opposite angles, then the parallelogram is a rhombus.
If a parallelogram is both a rectangle and a rhombus,
then the parallelogram is a square.
In the table below, write the name of the quadrilateral that BEST matches the
information that is checked. Choose from the following list:
rectangle
rhombus
square
Quadrilateral
that BEST
matches the
information
1. __________
Parallelogram
with a
diagonal that
Parallelogram
bisects a
Parallelogram with one pair Parallelogram
of congruent
with
pair of
with
Parallelogram
consecutive perpendicular
opposite
congruent
with one
angles
sides
diagonals
diagonals
right angle
X
2. __________
3. __________
X
X
X
4. __________
X
5. __________
X
6. __________
X
X
7. __________
X
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
6-42
Holt McDougal Geometry
8. 1
2. No; from the given information, you can
conclude only that ABCD is a rhombus.
3. Both pairs of opposite sides are ≅, so
STUV is a . STUV is a rectangle
with diags. ≅ → rect.
because
5. F
4. A
6. D
7. G
9. an infinite number
10. 3
11. 4
.
.
12. 3
13. (1, −1), (5, 1), (3, 7)
14. midsegment triangle
Reading Strategies
1. rectangle
2. rhombus
3. square
4. rectangle
5. square
6. rhombus
7. rhombus
6-6 PROPERTIES OF KITES AND
TRAPEZOIDS
Reteach
Practice A
1. valid
2. Not valid; need to know that MPQR is a
.
1. diagonals
2. angles
3. sides
4. 118°
3. valid
5. 3.25
6. 6
7. PQ ; SR
8. PS ; QR
.
4. Not valid; need to know that EFGH is a
5. rhombus
..
9. ∠S and ∠R or ∠P and ∠Q
6. rectangle, rhombus, square
10. diagonals or legs or base ∠S
7. rectangle
11. isosceles
8. rectangle, rhombus, square
12. congruent
14. ∠HEF ≅ ∠GFE; ∠EHG ≅ ∠FGH
Challenge
15. EH ≅ FG ; EG ≅ FH
7. a. The measure of each angle should be
108°. All the sides should be
congruent.
Practice B
1.
3.
5.
7.
9.
b. Results will vary.
8. Proceed as in Exercises 1–5. Draw ⊥
bisectors of all sides of pentagon; mark
intersection of bisectors and the circle as
the other 5 points of the decagon; draw
line segments.
55°
123°
98°
n = 11.5
a = 1.4
10. z =
9. Choices will vary.
2.
4.
6.
8.
22°
60 unit2
4.9
x = 12 or −12
19 or − 19
11. trapezoid midsegment
12. 19.45 m
Practice C
Problem Solving
1
(AC)(BD)
2
2. Yes; possible answer: the length of AE is
half the length of AC, and BE may be
1. Area =
1. Diagonals bisect each other, so the quad.
is a . The diagonals are ≅, so EFGH is
with diags. ≅ → rect.
a rect. because
.
13. base angles
.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Geometry