Question

We did not find results for: Consider the following proof of the Base Angles Theorem. Which statement should fill in the blank? PROOF: Given isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ , I can construct D , the midpoint of AC¯¯¯¯¯¯¯¯ . By the definition of a midpoint, I know that AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ . I can also construct BD←→ through points B and D . Because any line segment is congruent to itself by the reflexive property of congruence, BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ . __________________________. Corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠C . (1 point) Responses I also know that △ABC≅△ABC by the reflexive property of congruence I also know that △ABC≅△ABC by the reflexive property of congruence - incorrect I also know that by the definition of an angle bisector, ∠ABD≅∠CBD I also know that by the definition of an angle bisector, ∠ABD≅∠CBD - no response given I now have three pairs of sides congruent, so △ABD≅△CBD by the SAS Congruence Theorem I now have three pairs of sides congruent, so △ABD≅△CBD by the SAS Congruence Theorem - no response given I now have three pairs of sides congruent, so △ABD≅△CBD by the SSS Congruence Theorem.

Answer 1

To fill in the blank in the proof of the Base Angles Theorem, you should use the statement that involves the congruence of triangles based on pairs of sides being congruent.

The appropriate statement to fill in the blank is:

"I now have three pairs of sides congruent, so △ABD≅△CBD by the SAS Congruence Theorem."

This statement correctly follows from the previous information given in the proof and leads to the conclusion that the angles are also congruent (CPCTC).