9.5 Congruent Triangles and Similar Triangles 761corresponding angles are congruent, it follows that the third pair of corresponding
angles are also congruent:. By the AAA similarity theorem, we conclude
that.
Since the triangles are similar, the lengths of their corresponding sides are in
proportion. If we let represent the height of the flagpole, we can find by solving
the following proportion.
Height of the flagpole Distance from flagpole to mirror
Height of the woman Distance from woman to mirror h hABCEDC
B D
- a. ,,,,,b.20° c.3 ft
2.yes, by the SAS property 3.yes, by the SSS property 4. ,,
;,, 5.yes, by the AAA similarity theorem:
X X,,XYA XZBXAY XBZ 6. a. 6 b.11.25 7.500 ft
EG
JIFE
HJGF
IHFE
HJEG
JI GF
F H IHG IE JA EB DC FAB EDBC DFCA FEANSWERS TO SELF CHECKSSECTION 9.5 STUDY SET
VOCABULARY
Fill in the blanks.
- triangles are the same size and the same
shape. - When we match the vertices of with the
vertices of , as shown below, we call this
matching of points a. - Two angles or two line segments with the same
measure are said to be. - Corresponding of congruent triangles are
congruent. - If two triangles are , they have the same shape
but not necessarily the same size. - A mathematical statement that two ratios (fractions)
are equal, such as , is called a.
CONCEPTS- Refer to the triangles below.
18 x^49A 4 D B 4 E C 4 F
DEF
ABC
a. Do these triangles appear to be congruent?
Explain why or why not.
b. Do these triangles appear to be similar? Explain
why or why not.- a.Draw a triangle that is
congruent to
shown below. Label it
.
b. Draw a triangle that is similar
to, but not congruent to,
. Label it.
Fill in the blanks.
9.X ZYPQRXYZ
CDECDE MNO
ABC
CDE
Find each cross product and set them equal.
Do the multiplication.
To isolate h,divide both sides by 2.The flagpole is 50 feet tall.
h 502 h 1002 h5(20)h
5