Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 17: Geometry at Work 237

'GUI will be similar to 'EDI if ’G # ’E and ’U # ’D. The third angles are the pair

of vertical angles, and vertical angles are congruent, so you know m’GIU = m’EID. The

corresponding sides will be in proportion,

GU

DE

UI

DI

IG

IE

. When you know that two triangles are

similar, you can use a little squiggly line to show their relationship, like this: 'GUI~'EDI.

GU

I

D E

CHECK POINT

Write the proportion for each pair of similar triangles.

11. 'ABC~'XYZ


12. 'RST~'FED


13. 'PQR~'VXW

14. 'MLN~'LJK

15. 'ZXY~'BCA

Finding Missing Measurements

The primary reason that you want to know if a pair of triangles might be similar or congruent

is that it will help you find a measurement you need but can’t measure directly. If you know

two triangles are congruent, you know you have two identical sets of measurements. Suppose

nRST>nMNP. If RS = 12 feet and ST = 18 feet, you can find the length of MN, even though it’s

in the other triangle. Because corresponding parts of congruent triangles are congruent, MN =

RS = 12 feet.