501 Geometry Questions

CAUTION!When working with ratios and proportions, it doesn’t matter
which number goes in the numerator and which goes in the denominator
in the first ratio. However, when you are writing out the second fraction,
you must be sure to line up the corresponding parts correctly. For exam-
ple, looking at the triangles above, the following proportion is incorrect
since the corresponding sides are not lined up correctly:

BBCA≠EEDF

^160 ≠^1 x^2 

The illustration below shows all of the proportional relationships between
the similar triangles, ΔAEB and ΔCDB. Notice that since the triangles are sim-
ilar, with CBABand ABbeing twice as big as CB, it can be concluded that
the relationship between the other pairs of corresponding sides will also be 1:2.

Different sizes

Same shape

Different measurements, but in proportion

60 ° 30 °

60 °

30 °

B

1

C

D

A E

2

Corresponding Angles of Similar Triangles

Are Congruent (CASTC)

Corresponding Sides of Similar Triangles

Are Proportional (CPSTP)

A C

ABE CBD

CDB AEB

2 × BC = 1 × AB

2 × BD = 1 × BE

2 × CD = 1 × AE

x

F

E

D

12

10

C

B

A

6

501 Geometry Questions