1. J.L.

Given: Base ∡BAC and ∡ACB are congruent. Prove: ∆ABC is an isosceles triangle. When completed, the following paragraph proves that is congruent to making ∆ABC an isosceles triangle. Construct a perpendicular bisector from point B to . Label the point of intersection between this perpendicular bisector and as point D. m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector. ∡BDA is congruent to ∡BDC by the definition of congruent angles. is congruent to by _______1________. ∆BAD is congruent to ∆BCD by the _______2________. is congruent to because congruent parts of congruent triangles are congruent (CPCTC). Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

2. J.L.
3. J.L.

Its definitely not the first choice 1. Angle-Side-Angle (ASA) Postulate 2. congruent parts of congruent triangles are congruent (CPCTC) 1. congruent parts of congruent triangles are congruent (CPCTC) 2. Angle-Side-Angle (ASA) Postulate 1. the definition of a perpendicular bisector 2. Angle-Side-Angle (ASA) Postulate 1. congruent parts of congruent triangles are congruent (CPCTC) 2. the definition of a perpendicular bisector

4. J.L.

@Hero

5. J.L.

When completed, the following paragraph proves that line AB is congruent to line BC making ∆ABC an isosceles triangle. Construct a perpendicular bisector from point B to line AC. Label the point of intersection between this perpendicular bisector and line AC as point D. m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector. ∡BDA is congruent to ∡BDC by the definition of congruent angles. line AD is congruent to line DC by _______1________. ∆BAD is congruent to ∆BCD by the _______2________. line AB is congruent to line BC because congruent parts of congruent triangles are congruent (CPCTC). Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

6. aroub

1. the definition of a perpendicular bisector 2. Angle-Side-Angle (ASA) Postulate

7. J.L.

Thank you so much!!! I have a couple similar questions to this...do you think you can help me? I'm doing an online course so they haven't really explained this stuff properly.

8. aroub

Basically, perpendicular bisector is like a median.

9. aroub

Will try my best :) Just post them!