Geometry: An Interactive Journey to Mastery



Lesson 8: Proofs and Proof Writing

Proofs and Proof Writing

Lesson 8

Topic

x 3URRIZULWLQJLQJHRPHWU\

'H¿QLWLRQV

x deductive reasoning: 7KHSURFHVVRIHVWDEOLVKLQJWKHYDOLGLW\RIDUHVXOWE\ORJLFDOUHDVRQLQJ

x inductive reasoning: 7KHSURFHVVRI¿QGLQJSDWWHUQVDQGPDNLQJFRQMHFWXUHVEDVHGRQWKRVHSDWWHUQV

Summary

7KHWDVNRIZULWLQJDPDWKHPDWLFDOSURRILVDNLQWRWKHFKDOOHQJHRISUHVHQWLQJDFRQYLQFLQJFDVHWRDMXU\2QH

PXVWXVHSULVWLQHNQRZOHGJHQRWKLQJPRUHEDVHGRQLPPXWDEOHIDFWVQRWKLQJPRUHWRSUHVHQWDQDUJXPHQW

WKDWFDQQRWEHGRXEWHG,QWKLVOHVVRQZHOHDUQWKHDUWRIZULWLQJSURRIVLQJHRPHWU\

Example 1

*LYHQ ‘AECLVDULJKWDQJOH

BDAEC.

Prove: ‘#‘xy.

ͼ௘6HHFigure 8.1௘ͽ

Solution

i. ‘AECLVDULJKWDQJOHͼ௘JLYHQ௘ͽ

ii. ‘BDELVDULJKWDQJOHEHFDXVHBDAEC.

iii. AE BD| EHFDXVH‘AEC and ‘BDEDUHWZRVDPHVLGHLQWHULRUDQJOHVDGGLQJWRƒ

iv. ‘#‘xyEHFDXVHWKH\DUHDOWHUQDWHLQWHULRUDQJOHVIRUSDUDOOHOOLQHV

A

B

E D C

x y

Figure 8.1