Proof

Proof of Theorem 12-13

Given: ⊙ circle dot  O with intersecting chords A C ¯ eh c bar  and B D ¯ b d bar

Prove: m ∠ 1 = 1 2 ( m A B ⌢ + m C D ⌢ ) m angle , 1 equals , 1 half . open m , modified eh b with frown above . plus . m , modified c d with frown above , close

Begin by drawing auxiliary A D ¯ eh d bar  as shown in the diagram.

Image Long Description

Problem 1 Finding Angle Measures

Algebra What is the value of each variable?

1. 

   x = 1 2 ( 46 + 90 ) Theorem  12 - 13 x = 68 Simplify . table with 2 rows and 2 columns , row1 column 1 , x equals , 1 half , open 46 plus 90 close , column 2 cap theorem . 12 minus 13 , row2 column 1 , x equals 68 , column 2 cap simplify , . , end table

2. 

   20 = 1 2 ( 95 − z ) Theorem  12 - 14 40 = 95 − z Multiply each side by  2 . z = 55 Solve for  z . table with 3 rows and 3 columns , row1 column 1 , 20 , column 2 equals , 1 half , open 95 minus z close , column 3 cap theorem . 12 minus 14 , row2 column 1 , 40 , column 2 equals 95 minus z , column 3 cap multiplyeachsideby . 2 . , row3 column 1 , z , column 2 equals 55 , column 3 cap solvefor . z . , end table

✓ Got It?

1. What is the value of each variable?
   1. 
   2. 
   3.