11 making the connection language qi qiao is

11.
Making the Connection
[
Language
]
Qi qiao is
pronounced [che
–
che
–
au
.
].
2 2
2 2
2 2
2 2 2 2
2 4
2 4
2
4
2
2
2
2
484
CHAPTER 9
The Pythagorean Theorem
9.1

IMPROVING YOUR
V
ISUAL THINKING
SKILLS
Fold, Punch, and Snip
A square sheet of paper is folded vertically, a hole is punched
out of the center, and then one of the corners is snipped off.
When the paper is unfolded it will look like the figure at right.
Sketch what a square sheet of paper will look like when it
is unfolded after the following sequence of folds, punches,
and snips.
Fold once. Fold twice. Snip double-fold corner. Punch opposite corner.
12. Make a set of your own seven tangram pieces and create the Cat, Rabbit, Swan, and
Horse with Rider as shown on page 484.
13. Find the radius of circle Q. 14. Find the length of AC. 15. The two rays are tangent to
the circle. What ’ s wrong with
this picture?
16. In the figure below, point A 17. Which congruence shortcut 18. Identify the point of
is the image of point A after can you use to show that concurrency in QUO
a reflection over OT. What ABP DCP ? from the construction
are the coordinates of A ? marks.
19. In parallelogram QUID, m Q 2 x 5 ° and m I 4 x 55 ° . What is m U ?
20. In PRO, m P 70 ° and m R 45 ° . Which side of the triangle is the shortest?
PO
B D
A C
P
A
y
B
A
D
C
C
12 units
18 2 cm
4, 4 3
12.
15. Draw radii CD and CB.
ABC ADC 90°. For
quadrilateral ABCD 54°
90° m C 90° 360°, so
m C 126°. BD 126° but
126° 226° 360°.
Exercises 19, 20, 18
[
Language
]
The
figure names in these exercises
form a legal phrase: quid pro quo.
Quid pro quo means “ something
for something. ” It ’ s used to mean
the consideration for a contract,
that is, what each party gets out
of it (such as money or advan-
tage). A similar colloquial
expression is “ tit for tat. ”
EXTENSION
Have students show algebraically
that 3-4-5 is the only Pythagorean
triple of consecutive positive
integers.
LESSON 9.4
Story Problems
485
IMPROVING
V
ISUAL THINKING
SKILLS
9.3
7.1
5.5
4.3
9.1
4.5
6.2
3.7

L E S S O N
9.5
486
CHAPTER 9
The Pythagorean Theorem
We talk too much; we should
talk less and draw more.
JOHANN WOLFGANG
VON GOETHE
L E S S O N
9.5
Distance in Coordinate
Geometry
V
iki is standing on the corner of Seventh Street and 8th Avenue, and her brother
Scott is on the corner of Second Street and 3rd Avenue. To find her shortest sidewalk
route to Scott, Viki can simply count blocks. But if Viki wants to know her diagonal
distance to Scott, she would need the Pythagorean Theorem to measure across blocks.
You can think of a coordinate plane as a grid of streets with two sets of parallel
lines running perpendicular to each other. Every segment in the plane that is not
in the x - or y -direction is the hypotenuse of a right triangle whose legs are in the
x - and y -directions. So you can use the Pythagorean Theorem to find the distance
between any two points on a coordinate plane.