This document contains notes and instructions for geometry lessons on October 10th and 13th. It includes problems from a geometry drill, instructions to complete problems 11 and 12 from previous work, and learning objectives and examples for writing two-column geometric proofs using deductive reasoning.

1. GT Geometry Drill 10/10/13
Put CW/HW packet on the corner of
your desk
1. If the angles of a triangle are
represented by (3x) 0, x 0, (x+45) 0,
then what is the degree measure of
the largest angle?
2. If x=y+7 then what is the value of
(x-y)2 +8?

2. GT Geometry 10/10/13
• Take out drill paper from yesterday and
complete #11 and 12 see picture below for
#11
1
2
4
3
A B
CG
E
D
H
F

3. STW Write two-column
proofs & prove
geometric theorems by
using deductive
reasoning.
Objectives

4. Proofs
• Example 1
• Given:
• Prove:
D
BODmAOCm
31 mm
CB
A
O
3
21

5. Proof
Statement Reason
1. Given
2. Angle Addition
Postulate
3. Substitution Property
of Equality
4. Subtraction Property
of Equality
BODmAOCm.1
BODmmm
AOCmmm
32
21.2
3221.3 mmmm
31.4 mm

6. Check It Out! Example 2
Fill in the blanks to complete a two-column proof
of one case of the Congruent Supplements
Theorem.
Given: 1 and 2 are supplementary, and
2 and 3 are supplementary.
Prove: 1 3
Proof:

7. a. 1 and 2 are supp., and
2 and 3 are supp.
b. m 1 + m 2 = m 2 + m 3
c. Subtr. Prop. of =
d. 1 3

8. If a diagram for a proof is not provided, draw
your own and mark the given information on it.
But do not mark the information in the Prove
statement on it.
Helpful Hint

9. Use the given plan to write a two-column proof.
Example 3: Writing a Two-Column Proof from a Plan
Given: 1 and 2 are supplementary, and
1 3
Prove: 3 and 2 are supplementary.

10. Example 3 Continued
Statements Reasons
1. 1.
2. 2. .
3. . 3.
4. 4.
5. 5.
1 and 2 are supplementary.
1 3
Given
m 1 + m 2 = 180° Def. of supp. s
m 1 = m 3
m 3 + m 2 = 180°
3 and 2 are supplementary
Def. of s
Subst.
Def. of supp. s