Download Vocabulary - Hartland High School

Section 6.3 Use Similar Polygons
Goal  Use proportions to identify similar polygons.
In geometry, two polygons that have the same shape and same size are called _____________.
We learned that two polygons are CONGRUENT if and only if
___________________________ AND ___________________________ are equal.
C
B
F
G
E
A
H
D
However, two polygons are SIMILAR if and only if
a. COORESPONDING ANGLES ARE CONGRUENT
and
b. CORRESPONDING SIDE LENGTHS ARE PROPORTIONAL
Example 1: In the diagram, ABCD is similar to EFGH.
a. Symbols
C
B
b. Corresponding angles are congruent
A
F
G
D
c. Ratios of corresponding sides are equal.
E
H
d. Write the ratios of the corresponding side lengths in a statement of proportionality.
Scale Factor
The ratio of the lengths of the two corresponding sides of two similar polygons.
Example 2: Determine whether the polygons are similar. If they are, write a similarity
statement and find the scale factor of ABCD to JKLM.
a. Determine if the polygons are similar
b. Determine the scale factor of Figure A
to Figure B.
c. Find the perimeters of each polygon. What
is the scale factor between the perimeters.
Section 6.3 Use Similar Polygons
Example 3: In the diagram, ∆BCD  ∆RST. Find the value of x.
Checkpoint: In the diagram, FGHJ  LMNP.
1. What is the scale factor of LMNP to FGHJ?
2. Find the value of x.
Theorem 6.1: Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their
corresponding side lengths.
If KLMN  PQRS, then
KL  LM  MN  NK KL LM MN NK




PQ  QR  RS  SP
PQ QR
RS
SP
(Corresponding lengths are equal to the scale factor of similar polygons)
Example 4: In the diagram, ABCDE ~ FGHJK
a. Find the scale factor of ABCDE to FGHJK.
b. Find the value of x.
c. Find the perimeter of FGHJK and ABCDE.
Checkpoint: In the diagrams, ∆PQR  ∆WXY.
3. Find the perimeter of ∆WXY.
4. Find the length of median QS .