1. Lesson 16 Geometric Proofs
You use proofs everyday!!!
For instance, to persuade your parents to increase your allowance, your arguments must be presented logically and precisely.

2. Recall
SSS
SAS

3. Recall
ASA
AAS

4. Hypotenuse-Leg Congruence Theorem (HL)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

5. Are these triangles congruent?

6. In geometry we accept proofs as true
In geometry we accept proofs as true. A PROOF is a convincing argument that shows why a statement is true. In addition to applying theorems and definitions in proofs, the properties of real numbers are applied.
ΔJKL ≅ ΔJKL AB ≅ AB A ≅ A
Reflexive Prperty

7. Two Column Proof Statement Reasons
In this column we write the logical steps that lead us to the end result.
Step 1: Begin by listing the information given.
Step 2: Use information from the diagram.
Step 3: End the proof with the statement you are trying to prove.
For each statement, we must state a reason (theorems, definitions, and information).

8. Ex. 1 Write a two – column proof that shows that ΔJKL ΔNML
Statement
Reasons
1. JL NL
Given S
2. L is the midpoint of KM
Given
3. KL LM
3. def’n of midpoint S
4. JLK MLN
4. vertical angles thm A
5. ΔJKL ΔNML
SAS

9. Ex. 2 Write a two – column proof that shows that ΔABC ΔEDC.
Statement
Reasons S
1. AC EC
1. Given
2. AE  DB
2. Given S
3. DC BC
3. Given A
4.  ACB ≅ DCE = 90o
4. def’n of perp lines
5. ΔABC ≅ ΔEDC
5. SAS

10. 1. _____________________ 2. _____________________
Ex. 3 Write a two – column proof that shows that ΔACB ≅ ΔDBC. B D
Given: BD ≅ AC
Prove: ACB ≅ ΔDBC A C
Statement
Reason
BD ≅ AC
BD ll AC
DBC ≅ ACB
BC ≅ BC
ΔACB ΔDBC
1. _____________________
2. _____________________
3. _____________________
4. _____________________
5. _____________________

11. Class Work
P #34-36
P. 247 #32-35
P.248 #36