Answer:
(C) Base angle theorem
Step-by-step explanation:
Given: JKLM is an isosceles trapezoid, KL ∥ JM
Prove: KM ≅ JL
Proof:
Statements Reasons
1. JKLM is an isosceles trapezoid, KL ∥ JM Given
2. JK ≅ LM definition of isosceles trapezoid
3. KL ≅ KL reflexive property
4. ∠JKL ≅ ∠MLK Base angle theorem (base=LK)
5. △JKL ≅ △MLK SAS rule
6. KM ≅ JL CPCTC
Hence proved.
therefore, option C is correct.
The missing reason for statement 4, is: C. base angles theorem.
The base angle theorem states that the two base angles in an isosceles triangle that are opposite the congruent sides are equal in measure or congruent.
Thus, ∠JKL and ∠MLK are base angles of the identified isosceles triangle, therefore, the missing reason for statement 4, is: C. base angles theorem.
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