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PLEASE HELP!!!! In ∆ABC shown below, ∡BAC is congruent to ∡BCA.

Mathematics
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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.
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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

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Other answers:

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.
1. the definition of a perpendicular bisector 2. Angle-Side-Angle (ASA) Postulate
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.
Basically, perpendicular bisector is like a median.
Will try my best :) Just post them!

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