Question

given: jklm is an isosceles trapezoid, (overline{kl} parallel overline{jm})
prove: (overline{km} cong overline{jl})
what is the missing reason in step 4?

statements	reasons
2. (overline{jk} cong overline{lm})	2. definition of isosceles trapezoid
3. (overline{kl} cong overline{kl})	3. reflexive property
4. (angle jkl cong angle mlk)	4. ?
5. (\triangle jkl cong \triangle mlk)	5. sas (cong) theorem
6. (overline{km} cong overline{jl})	6. cpctc

options: definition of linear pair, definition of congruence, base angles theorem, sufficient base angles theorem

Explanation:

In an isosceles trapezoid, the base angles are congruent. Since \( \overline{KL} \parallel \overline{JM} \), \( \angle JKL \) and \( \angle MLK \) are base angles of the isosceles trapezoid \( JKLM \). The base angles theorem states that base angles of an isosceles trapezoid are congruent. The other options don't apply: "definition of linear pair" is about adjacent angles forming a line, "definition of congruence" is about equal measures (not specific to trapezoid angles), and "sufficient base angles theorem" is not a standard term here. So the missing reason is the base angles theorem.

Answer:

base angles theorem