Triangle Proofs PracticeComplete this assessment to review what you’ve learned. It will not count toward your grade.5 of 5 5 of 5 ItemsQuestionUse the image to answer the question. Beatrix is working to prove the Base Angles Theorem. They start with an isosceles triangle △ABC with AB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯. Then they construct AD¯¯¯¯¯¯¯¯, the angle bisector of point A. They know they are supposed to prove that two triangles are congruent in order to prove the Base Angles Theorem. They show how △ABD≅△ACD by the SAS Congruence Theorem. They aren’t sure how to finish the proof. Help them construct a viable argument. What should Beatrix do next? Option #1: Show that ∠BAD≅∠CAD by the definition of an angle bisector.Option #2: Show that ∠C≅∠A by the CPCTC Theorem.Option #3: Show that ∠B≅∠C by the CPCTC Theorem.Option #4: Show that BD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ by the definition of a midpoint.(1 point)Option #?

Question

Triangle Proofs PracticeComplete this assessment to review what you’ve learned. It will not count toward your grade.5 of 5 5 of 5 ItemsQuestionUse the image to answer the question. Beatrix is working to prove the Base Angles Theorem. They start with an isosceles triangle △ABC with AB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯. Then they construct AD¯¯¯¯¯¯¯¯, the angle bisector of point A. They know they are supposed to prove that two triangles are congruent in order to prove the Base Angles Theorem. They show how △ABD≅△ACD by the SAS Congruence Theorem. They aren’t sure how to finish the proof. Help them construct a viable argument. What should Beatrix do next?  Option #1: Show that ∠BAD≅∠CAD by the definition of an angle bisector.Option #2: Show that ∠C≅∠A by the CPCTC Theorem.Option #3: Show that ∠B≅∠C by the CPCTC Theorem.Option #4: Show that  BD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ by the definition of a midpoint.(1 point)Option #?

GPT-4o mini · Answer

To help Beatrix finish the proof of the Base Angles Theorem after establishing that triangles \( \triangle ABD \cong \triangle ACD \) by the SAS Congruence Theorem, the next step is to show the corresponding angles are congruent.

In this case, since \( AD \) is the angle bisector of \( \angle A \), Beatrix should show that \( \angle BAD \cong \angle CAD \) due to the definition of an angle bisector, which states that an angle bisector divides the angle into two equal parts.

Thus, the correct option for Beatrix to choose is:

Option #1: Show that \( \angle BAD \cong \angle CAD \) by the definition of an angle bisector.

From that point, by using the fact that \( \triangle ABD \cong \triangle ACD \), she can then conclude that the base angles \( \angle B \cong \angle C \).