Geometry
Notes
Name_________________________
Geometry – Unit 6 Warm up 2
Solve the proportion.
3 2
1.

x 7
2.
2
4

x 1 x  6
3. The measures of the angles in a triangle are in the extended ratio 2 : 15 : 19. Find the measure of
each angle.
4. The perimeter of a rectangle is 84 feet. The ratio of the width to the length is 2 : 5. Find the
length and the width.
5. Find the geometric mean of 1 and 100
.
Using Similar Polygons
similar polygons –
written as:
Examples
1. In the diagram, RST ~ XYZ.
a. List all the pairs of congruent angles.
T
Z
15
25
X
b. Check that the ratios of corresponding side lengths are equal.
R
18
30
Y
12
S
20
c. Write the ratios of the corresponding side lengths in a statement of proportionality.
Scale Factor: _____________________________________________________________
2. Determine whether the polygons are similar.
If they are, write a similarity statement and find
the scale factor of ZYXW to FGHJ.
16
F
J
20
Z
W
12
20
15
H 25
24
X
G
30
Y
3. In the diagram, DEF ~ MNP. Find the value of x.
N
E
9
D
x
12
12
F M
20
16
P
Perimeters of Similar Polygons:
If KLMN ~ PQRS, then
KL  LM  MN  NK KL LM MN NK




.
PQ  QR  RS  SP PQ QR RS SP
Examples
4. In the diagram, ABCDE ~ FGHJK.
F
a. Find the scale factor of FGHJK to ABCDE.
A
b. Find the value of x.
10
15
G
B
x
9
C
H
18
12
E
D
K
15
J
c. Find the perimeter of ABCDE.
5. In the diagram, TPR ~ XPZ. Find the length of PS.
Note: In similar triangles all aspects of a triangle are proportional. This includes the_____________.
New vocab alert: The altitude is:
X
T
6
S
6
P
8
20
Y
8
R
Z
6. A town is building a new swimming pool. An Olympic pool is rectangular with length 50 meters and
width 25 meters. The new pool will be similar in shape, but only 40 meters long.
a. Find the scale factor of the new pool to an Olympic pool.
b. Find the perimeter of an Olympic pool and the new pool.