Question

Select the correct answer. Given: ∆ABC is an isosceles triangle where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ∆ABC be an isosceles triangle where AB = BC. given 2. Create point D on side so that bisects ∠ABC as shown. constructing an angle bisector 3. m∠ABD = m∠CBD 4. BD = BD Reflexive Property of Equality 5. ∆ABD ≅ ∆CBD SAS 6. m∠BAC = m∠BCA Corresponding angles of congruent triangles have equal measures. What is the reason for statement 3 in this proof? A. definition of angle bisector B. Alternate Interior Angles Theorem C. Corresponding Angles Theorem D. Corresponding angles of congruent triangles are congruent.

Answer 1

Answer: A. definition of angle bisector

Step-by-step explanation:

Since, An angle bisector always divides an angle into two congruent angles.

Given: ∆ABC is an isosceles triangle

Where AB = BC

Prove: m∠BAC = m∠BCA

                       

              Statement                                                          Reason

1. Let ∆ABC be an isosceles triangle where AB = BC  1. Given

2. Create point D on side so that bisects ∠ABC          2. constructing an                              

                                                                                         angle bisector

3.m∠ABD = m∠CBD                                                        3. definition of angle                          

                                                                                          bisector

4. BD = BD                                                                       4.Reflexive Property of  

                                                                                          Equality

5.∆ABD ≅ ∆CBD                                                             5. SAS

6. m∠BAC = m∠BCA                                                       6. CPCTC