Question

given: j k l m is an isosceles trapezoid, \\( \overline { k l } \parallel \overline { j m } \\) prove: \\( \overline { k m } \cong \overline { j l } \\) what is the missing reason in step 4?

statements	reasons
2. \\( \overline { j k } \cong \overline { l m } \\)	2. definition of isosceles trapezoid
3. \\( \overline { k l } \cong \overline { k l } \\)	3. reflexive property
4. \\( \angle j k l \cong \angle m l k \\)	4.?
5. \\( \triangle j k l \cong \triangle m l k \\)	5. sas \\( \cong \\) theorem
6. \\( \overline { k m } \cong \overline { j l } \\)	6. cpctc

definition of linear pair
definition of congruence
base angles theorem
sufficient base angles theorem

Explanation:

Step1: Recall properties of isosceles trapezoid

In an isosceles trapezoid \(JKLM\) with \(KL\parallel JM\), the base - angles are congruent.

Step2: Analyze the angles

\(\angle JKL\) and \(\angle MLK\) are base - angles of the isosceles trapezoid \(JKLM\). By the base - angles theorem of isosceles trapezoid, \(\angle JKL\cong\angle MLK\)

Answer:

base angles theorem