Strategy Focus
19 Draw a Diagram
Lesson
MATH FOCUS: Similar and Congruent Figures
Learn
Read the Problem The Visitor Center at Ride City is making a map of the park. The park is
in the shape of an isosceles trapezoid with bases of length 10,000 feet
and 16,000 feet and sides of length 5,000 feet. On the map, the longer
base of the trapezoid will be 64 inches long. What should the height of
the trapezoid be on the map?
Reread Check that you have correctly understood the problem.
What is the problem about?
●
What details do you know?
●
What are you asked to find?
●
Mark
the Text
Search for Information Find the details that you need in the problem.
Record Write the information that you found.
The lengths of the bases of the actual park are
and
.
The lengths of the sides of the actual park are
.
The length of the longer base of the trapezoid on the map is
.
© Triumph Learning. OT114eIW19
Use this information to help you decide how to solve the problem.
156 Unit 5 Using Geometry and Measurement
and
Decide What to Do
You know the shape and dimensions of the actual park. You also know
one dimension of the shape on the map of the park.
Ask How can I find the height of the trapezoid on the map?
I can use the strategy Draw a Diagram to show the park.
●
Next, I can use the Pythagorean theorem to find the height of the
actual trapezoid. Then I can use a proportion to find the height of
the trapezoid on the map.
●
Use Your Ideas
Draw a diagram of the park and label the dimensions you know.
Step 1
Use the Pythagorean theorem
to find the height of one of the
congruent right triangles. Label
the height on the diagram.
10,000 ft
5,000 ft
3,000 ft
a +b =c
2
2
5,000 ft
h
2
16,000 ft
3,000 ft
3,0002 + h2 = 5,0002
9,000,000 + h2 = 25,000,000
h2 = 25,000,000 − 9,000,000
h2 = 16,000,000
Step 2
The trapezoid
is made up of a
rectangle and
two congruent
right triangles,
so you know the
base of each
triangle must be
3,000 feet.
h=
Use what you know to write and solve a proportion.
Height on map
Base on map
____________________
​ 
  
   ​= ___________________
​ 
  
   ​
Height of actual trapezoid
Base of actual trapezoid
a   ​ = ______
64   ​ 
​ 16,000
​ _____
4,000
16,000a = 256,000
a = 16
The height of the trapezoid on the map should be
© Triumph Learning. OT114eIW19
Review Your Work
inches.
Check that your answer is reasonable.
Relate How did writing the dimensions on the diagram help you?
157