HONORS GEOMETRY
7.2. Similar Polygons
Do Now:
• The perimeter of a rectangle is 98 feet. The ratio of its
length to its width is 5:2. Find the area of the rectangle.
• A survey of club involvement showed that, of the 36
students surveyed, the ratio of French Club members to
Spanish Club members to Drama Club members was
2:3:7. How many of those surveyed participate in Spanish
Club? Assume that each student is active in only one
club.
Homework
• Questions?
• Comments?
• Confusions?
• Concerns?
• ASK ASK ASK ASK!
Similar Polygons
• Two polygons are similar if and only if their corresponding
angles are congruent and their corresponding sides are
proportional.
• I.E. The same shape but not necessarily the same size.
So…..
• To get triangle congruence we have SSS, SAS, AAS,
ASA….
• Which of the problem ones will actually yield similar
triangles?
Realize:
• Just like order matters with congruent triangles, order
matters with similar polygons!
Example One:
• If △ 𝐹𝐺𝐻~ △ 𝐽𝐾𝐿, list all pairs of congruent angles, and
write a proportion that relates the corresponding sides.
You Try!
• Quadrilateral 𝑁𝑃𝑄𝑅 ~ Quadrilateral 𝑈𝑉𝑆𝑇. List all pairs of
congruent angles, and write a proportion that relates the
corresponding sides.
Scale Factor:
• The ratio of the lengths of the corresponding sides of two
similar polygons.
• Realize: The scale factor depends on the order of
comparison
Example Two:
• What is the scale factor of ∆𝐴𝐵𝐶 to ∆𝑋𝑌𝑍?
• What is the scale factor of ∆𝑋𝑌𝑍 to ∆𝐴𝐵𝐶?
Example Three:
Example Four:
• Are the following pairs of polygons similar? If so, write a
similarity statement and state the scale factor.
You Try!
• Are the following similar polygons? If so write a similarity
statement and state the scale factor
Example Five:
• Quadrilateral 𝐴𝐶𝐷𝐹~ Quadrilateral 𝑉𝑊𝑌𝑍. Find the values
of x and y.
Example Six:
• Polygon 𝐴𝐵𝐶𝐷𝐸~Polygon 𝐺𝐻𝐽𝐾𝐿. Find the missing
values.**Don’t worry about g**
Do Now:
• Look at your test– where do you go wrong? Do you have
questions? Are you confused?
You Try!
• Find x, y and z if polygon 𝑄𝑀𝑁𝑃~polygon 𝑈𝑅𝑆𝑇
∆𝐴𝐵𝐶~∆𝐴′ 𝐵′ 𝐶′
Perimeters of Similar Polygons
• If two polygons are similar, then their perimeters are
proportional to the scale factor between them.
Example Seven:
• Polygon ABCDE~ Polygon PQRST. Find the scale factor
of ABCDE to PQRST and the perimeter of each polygon.
Example Eight:
• If polygon 𝐴𝐵𝐶𝐷𝐸~ polygon 𝑅𝑆𝑇𝑈𝑉, find the scale factor
of 𝐴𝐵𝐶𝐷𝐸 to 𝑅𝑆𝑇𝑈𝑉 and the perimeter of each polygon
You Try!
• If polygon 𝐴𝐵𝐶𝐷𝐸~ polygon 𝑃𝑄𝑅𝑆𝑇 find the scale factor of
ABCDE to PQRST and the perimeter of each polygon.
Practice Problems
• Try some on your own/in your table groups
• As always don’t hesitate to ask questions if you are
confused and/or talk to your tablemates– they are your
greatest resource!
Exit Ticket:
• Find x and y if triangle ACT is similar to triangle ODG