Name______________________________________________ Class___________________
Congruent vs. Similar Polygons: Day 1
Congruent polygons:
Symbol for congruent:
Congruent polygons
∆ABC  ∆DEF
“Hash” marks show:
“Hoops” show”
Angles - Corresponding angles are congruent:
A  
, B  
, and C  
Sides - Corresponding sides are congruent:
EXAMPLE 1: Finding Measures of Congruent Polygons
Given that ABCD  WXYZ, mark the corresponding angles and sides. Then find the
measurement of side XY.
What is the measurement of XY?
NOW YOU TRY IT!
1) Given that ∆ABC  ∆LMN, mark the corresponding angles and sides. Then find the
unknown angle measurements.
Similar polygons:
Symbol for similar:
Similar Polygons
∆LMN ~ ∆PQR
Angles: Corresponding angles are congruent:
L  
, M  
, and N  
Sides: Ratios of corresponding sides are equal:
EXAMPLE 2: Finding the Ratio of Lengths
Given that ∆ABC ~ ∆DEF, mark the congruent angle and find the ratio of the lengths of the
corresponding sides of ∆ABC to ∆DEF.
Lengths of corresponding sides
written as a ratio
Simplify (if needed)
NOW YOU TRY IT!
2) Given that XYZ ~ EFG, mark the congruent angles and find the ratio of the lengths of the
corresponding sides.
Lengths of corresponding sides
written as a ratio
Simplify (if needed)
EXAMPLE 3: Checking for Similarity
A photograph of a rug in a catalog is 10 centimeters long and 7 centimeters wide. The
actual rug is 171 centimeters long and 92 centimeters wide. Are the photograph of the rug
and the actual rug similar figures? (Draw a picture to help you out)
NOW YOU TRY IT!
3) A landscape architect is planning a memorial 18 feet long and 15 feet wide. A
rectangular blueprint of the garden has a length of 12 inches long and 10 inches wide. Are
the garden and the blueprint similar figures?