SOLUTION: Question:How can I write a formal proof of the theorem. "If the base angles of a triangle are congruent, then the triangle is isosceles" This was my proof that was incorrect.

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Question 49791: Question:How can I write a formal proof of the theorem.
"If the base angles of a triangle are congruent, then the triangle is isosceles"
This was my proof that was incorrect.
Given: angle DAB=DAC (told not base angles)
STATEMENTS REASONS
1. angleDAB=angleDAC 1. Given
2. DA-DA 2. Reflexive Property
3. Triangle BAD=Triangle CAB 3. SSS
4. BD=ED 4. CPCTC
5. angleBAD=angle CAD 5. Converse Base Angle Theorem
6. AD bisect BC 6. Def. of an Isosceles Triangle
7. triangle ABD=Triangle ACD 7. Isosceles Triangle
Could you please show me the correct way to prove this theorem?
Found 2 solutions by venugopalramana, AnlytcPhil:
Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!
SEE MY COMMENTS BELOW..
Question:How can I write a formal proof of the theorem.
"If the base angles of a triangle are congruent, then the triangle is isosceles"
This was my proof that was incorrect.
Given: angle DAB=DAC (told not base angles)
NO...FIRST NAME THE TRIANGLE
GIVEN....
LET ABC BE THE TRIANGLE WITH A AS VERTEX
BASE ANGLES ABC AND ACB ARE SAME.THAT IS
ANGLE ACB = ANGLE ABC
TO PROVE....
ABC IS ISOCELLES TRIANGLE..
THAT IS AB=AC
CONSTRUCTION...
DRAW AD PERPENDICULAR TO BC.D IS ON BC.
PROOF.....
STATEMENTS REASONS
IN TRIANGLES DAB AND DAC
1. angleDAB=angleDAC ...NO.....ANGLE DBA=ANGLE DCA.... Given
2. DA-DA....NO .....AD=AD.... Reflexive Property
3. Triangle BAD=Triangle CAB..........NO 3. SSS............NO
ANGLE BDA=90=ANGLE CDA ....BY CONSTRUCTION
4. HENCE THE 2 TRIANGLES DAB AND DAC ARE CONGRUENT....AAS
HENCE AB=AC..BY CONGRUENCE PROPERTY.
HENCE THE TRIANGLE ABC IS ISOCELLES.

5. angleBAD=angle CAD 5. Converse Base Angle Theorem
6. AD bisect BC 6. Def. of an Isosceles Triangle
7. triangle ABD=Triangle ACD 7. Isosceles Triangle
Could you please show me the correct way to prove this theorem?

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

Question:How can I write a formal proof of the theorem.

"If the base angles of a triangle are congruent, then 
the triangle is isosceles"

Could you please show me the correct way to prove this 
theorem?

--------------------------------------------

Given: DABC, ÐA @ ÐC 

     B
    / \
   /   \
  /     \
 /       \
A¯¯¯¯¯¯¯¯¯C

Draw altitude BD 

     B
    /|\
   / | \
  /  |  \
 /   |   \
A¯¯¯¯D¯¯¯¯C


STATEMENTS                       REASONS

1. ÐA @ ÐC                       1. Given

2. BD @ BD                       2. Reflexive Property

3. BD ^ AC                       3. Altitude is ^ the base it's
                                    drawn to   

4. ÐADB @ ÐCDB = 90°             4. BD ^ AC 

5. DBAD @ DBCD                   5. AAS

6. BA @ BC                       6. CPCTC

7. DABC is isoceles              7. It has two congruent sides  

Edwin
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