a) corresponding angles are congruent, and
b) corresponding lengths are proportional ( the ratios are the same )
If
ABC ~
KLM, then:
1. m
A
= mK; mB
= mL; mC
= m M 2.
Similarity UP
If two figures are similar (~),
then:
a)
corresponding angles are congruent, and
b)
corresponding lengths are proportional ( the ratios are the same )
If ABC ~
KLM, then:
1. mA
= mK; mB
= mL; mC
= m M
2.
Example
Given: ABC
~ DEF;
mB = 90°; AB = 9; AC = 41; BC = 40;
EF = 60
Find: mE,
DF, DE 
Solution
1. Find mE
Since ABC
~
DEF,
then mE
= mB = 90°
( corresponding angles are
congruent or corresponding angle
measures are equal )
2. Find DF
a)
b) 
corresponding lengths are proportional
( substitute AC, BC, EF)
c) 41
60 = 40DF
( cross-multiply ) d) 
DF = 61.5
3. Find DE
DE40 = 960
Answer: mE
= 90°; DF = 61.5; DE = 13.5