1. The document provides instructions and examples for a geometry drill involving proofs about angles, polygons, and supplementary angles. 2. It includes problems about finding the measure of angles in a triangle, evaluating expressions with variables, defining adjacent angles, identifying polygons, and writing two-column proofs. 3. The objectives are to write two-column proofs and prove geometric theorems using deductive reasoning, with examples provided of filling in the statements and reasons of proofs.

1. GT Geometry Drill 10/27/14
Put CW/HW 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. Geometry Drill
3. What are adjacent angles?
4. Given: A hexagon is a six sided
polygon.
T/F If a polygon has six sides, then it
is a hexagon
T/F Every hexagon is a polygon
T/F Every figure is a hexagon

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

4. Proofs
• Example 1
• Given:
• Prove:
mAOCmBOD
m1m3
D
B C
A
O
3
1 2

5. Proof
Statement Reason
1. Given
2. Angle Addition
Postulate
3. Substitution Property
of Equality
4. Subtraction Property
of Equality
1.mAOCmBOD
m m m AOC
    
2. 1 2
    
2 3
m m m BOD
3.m1m2 m2m3
4.m1m3

6. Helpful Hint
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.

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

8. Example 3 Continued
Statements Reasons
1 and 2 are supplementary.
1  3
1. 1.
2. 2. .
3. . 3.
4. 4.
5. 5.
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

12. • Given : m< ALC = m< PLS
• Prove: m < PLA = m< SLC
P
A S C
L #

13. Geometry Objective
•STW review for
the test
Thursday!