Triangle ABC is shown с
Given: Triangle ABC is isosceles. Point D is the midpoint of AC.
Prove: BAC = BCA
Place reasons in the table to complete the proof.
Reasons
1. Given
Statements
1. Triangle ABC is isosceles.
D is the midpoint of AC
2. 2. ADDC
3 3 BA = BC
2. Definition of midpoint
3. Definition of isosceles triangle
4. A single line segment can be drawn between
any two points
5.
4. 4. BD exists
5. 5. BD BD
6. 6. AABD
shyap
6
7.7 /BAC/BCA
7
Symmetric
Reflexive
AA

Step-by-step explanation:

              Statements                                            Reasons

1). Triangle ABC is isosceles. D is          1). Given

   the midpoint of AC.

2). AD ≅ DC                                            2). Definition of midpoint

3). BA ≅ BC                                             3). Definition of an isosceles

                                                                     triangle.

4). BD exists                                            4). A single line segment can be

                                                                    drawn between any two points.

5). BD ≅ BD                                            5). Reflexive property

6). ΔABD ≅ ΔCBD                                 6). By SSS property of congruence

7). ∠BAC ≅ ∠BCA                                  7). CPCTC