Question

Prove: the base angles of an isosceles triangle are congruent. the two-column proof with missing statement proves the base angles of an isosceles triangle are congruent: statement reason 1. segment bd is an angle bisector of ∠abc. 1. by construction 2. ∠abd ≅ ∠cbd 2. definition of an angle bisector 3. 3. reflexive property 4. δabd ≅ δcbd 4. side-angle-side (sas) postulate 5. ∠bac ≅ ∠bca 5. cpctc which statement can be used to fill in the numbered blank space? line segment bd ≅ line segment ac line segment bd ≅ line segment bd line segment ac ≅ line segment ac line segment ad ≅ line segment dc

Answer 1

The missing statement to prove that the base angles of an isosceles triangle are congruent is 'Segment AD ≡ Segment DC', which demonstrates the sides of the triangle opposite to the base are equal.

Step-by-step explanation:

To prove the base angles of an isosceles triangle are congruent, we are given a two-column proof with a missing statement.

We can fill in the missing statement with segment AD ≡ segment DC, which corresponds to the sides of the triangle that are not part of the base.

Statement 3 can then be completed in our two-column proof.

Segment BD is an angle bisector of ∠ABC. - By construction

∠ABD ≡ ∠CBD - Definition of an angle bisector

Segment AD ≡ Segment DC - Reflexive Property

ΔABD ≡ ΔCBD - Side-Angle-Side (SAS) Postulate

∠BAC ≡ ∠BCA - CPCTC (Corresponding Parts of Congruent Triangles are Congruent)