Pre-Algebra Chapter 9

Similar Triangles and
Indirect Measurement
Vocabulary
• similar triangles
• indirect measurement
• Identify corresponding parts and find missing measures of similar triangles.
• Solve problems involving indirect measurement using similar triangles.
can similar triangles be used to create patterns?
The triangle at the right is called Sierpinski’s triangle.
The triangle is made up of various equilateral
triangles. The following activity investigates
patterns similar to the ones in Sierpinski’s triangle.
Step 1 On dot paper, draw a right triangle
whose legs measures 8 and 16 units.
Find the measure of each angle.
Step 2 Count to find the midpoint of each side of the triangle.
Then connect the midpoints of each side.
Step 3 Shade the middle triangle.
Step 4 Repeat this process with each non-shaded triangle. Your triangles
will resemble those shown below.
Step 1 Step 2 Step 3 Step 4
a. Compare the measures of the angles of each non-shaded triangle to
the original triangle.
b. How do the lengths of the legs of the triangles compare?
Reading Math
Similar Symbol
The symbol is read
is similar to.
CORRESPONDING PARTS Triangles that have the same shape but not
necessarily the same size are called similar triangles . In the figure below,
ABC is similar to XYZ. This is written as ABC XYZ.
Y
B
A
C
X
Z
Similar triangles have corresponding angles and corresponding sides. Arcs are
used to show congruent angles.
B
Y
A
C
X
Z
Corresponding Angles
A ↔ X B ↔ Y C ↔ Z
Corresponding Sides
AB ↔ XY BC ↔ YZ AC ↔ XZ
Lesson 9-7 Similar Triangles and Indirect Measurement 471