SOLUTION: Prove : that triangle ABC is Isosceles. Where AD __l__ BC Can you tell me where I went wrong and what is the correct answer? ~ 1: < BAD = angle CAD

Algebra ->  Triangles -> SOLUTION: Prove : that triangle ABC is Isosceles. Where AD __l__ BC Can you tell me where I went wrong and what is the correct answer? ~ 1: < BAD = angle CAD       Log On


   

Question 601480: Prove : that triangle ABC is Isosceles. Where AD __l__ BC
Can you tell me where I went wrong and what is the correct answer?
~
1: < BAD = angle CAD reason Given

__ ___
2: AD __l_ BC reason Given

3angleBDA and angle are right angles = reason Definition of perpendicular

4 < BDA is congruent to CDA reason: transfer property of equality

5 BD is congruent to CD reason Definition of a bisector therom

6 AD is congruent to CD reason Reflexive property of congruency

7angle ABC is congruent to angle ADC reason SAS congruency of triangles

8Angle ABC is congruent to ACD of a congruent triangle are congruent.
8BReason: reason corresponding parts of a congruent triangle are congruent.

9. ABC is ab isosceles triangle reason Definition of an isosceles triangle is a triangle that has 2 angles and 2 sises that are congruent.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
You have a number of incorrect statements.
You have incorrect use of reflexive property of congruence.
The reflexive property says things are congruent to THEMSELVES!
Incorrect use of transfer property; not needed. 5 is wrong; 
don't use "bisector" theorem.  Triangles are isosceles by definition
if only two sides are congruent. Use ASA, not SAS.
Here is a correct proof:

 

1. ∠BAD ≅ ∠CAD        Given
2.   AD ⊥ BC          Given
3. ∠BDA ≅ ∠CDA        Both are right angles by 2
4.   AD ≅ AD          Reflexive property
5. ᐃADB ≅ ᐃABC        Angle-Side-Angle
6.   AB ≅ AC          Corresponding parts of
                        congruent triangles
7. ᐃABC is isosceles  Two sides are congruent.

Edwin