Page 239 - Algebra 1

Finding Measures in Similar Figures
Example
1
Reading Math
The notation m ∠Q is read “the measure of angle Q.”
PQRS ∼ WXYZ
a. Find m∠Q and m∠W.
SOLUTION
Q
∠Q and ∠X correspond, so they are
equal, and m∠Q = 80°. ∠W and ∠P correspond, so they are equal and m∠W = 120°.
70°
P
120° 3
a
X
2
S 6 R Z b Y
W
80°
5
b. Find the scale factor of PQRS to WXYZ. SOLUTION
−− −−−
PS and WZ correspond, so the scale factor of PQRS to WXYZ is WZ = 2
__ PS 3 .
c. Use the scale factor to find QR and ZY.
SOLUTION
Hint
To avoid confusion,
write the ratios with all sides from one figure in the numerator and all corresponding sides from the other figure in the denominator.
All corresponding side lengths must be in a ratio of 3 to 2. QR corresponds
−−−− −−
with XY and ZY corresponds with SR. PS = QR PS = SR
__ __ WZ XY WZ ZY
_3 = _a _3 = _6 25 2b
2a = 15 3b = 12 a = 7.5 b = 4
So, QR = 7.5 and ZY = 4.
Another application of proportional reasoning is indirect measurement.
Indirect measurement involves using similar figures to find unknown lengths.
−−−
Example
2
Using Indirect Measurement
A radio tower casts a shadow 10 feet long. A woman who is 5.5 feet tall casts a shadow 4 feet long. The triangle drawn with the tower and its shadow is similar to the triangle drawn with the woman and her shadow. How tall is the radio tower?
SOLUTION Set up a proportion to solve the problem.
__ 10 = x
4 5.5 10(5.5) = 4 · x
55 = 4x 13.75 = x
x feet
5.5 feet
224 Saxon Algebra 1
The radio tower is 13.75 feet tall.
10 feet
4 feet