Math

QuestionQuadrilateral ABCD is congruent to HJKL. Complete: JK\overline{J K} \cong options: a. BC\overline{B C}, b. CB\overline{C B}, c. HL\overline{H L}, d. KJ\overline{K J}.

Studdy Solution

STEP 1

Assumptions1. Quadrilateral ABC is congruent to Quadrilateral HJK. The order of vertices in the congruent statement matters. For example, if AB\overline{A B} is congruent to HJ\overline{H J}, then BA\overline{B A} would be congruent to JH\overline{J H}, not HJ\overline{H J}.

STEP 2

The congruence of quadrilaterals implies that corresponding sides and angles are congruent. Therefore, if Quadrilateral ABC is congruent to Quadrilateral HJK, then AB\overline{A B} is congruent to HJ\overline{H J}, BC\overline{B C} is congruent to JK\overline{J K}, CD\overline{C D} is congruent to KL\overline{K L}, and A\overline{ A} is congruent to H\overline{ H}.

STEP 3

Now, let's analyze each statementa. JKBC\overline{J K} \cong \overline{B C}This statement is true because BC\overline{B C} is the corresponding side to JK\overline{J K} in the congruent quadrilaterals.

STEP 4

b. JKCB\overline{J K} \cong \overline{C B}This statement is false because CB\overline{C B} is not the corresponding side to JK\overline{J K}. The corresponding side to JK\overline{J K} is BC\overline{B C}, not CB\overline{C B}.

STEP 5

c. JKHL\overline{J K} \cong \overline{H L}This statement is false because HL\overline{H L} is not the corresponding side to JK\overline{J K}. The corresponding side to JK\overline{J K} is BC\overline{B C}, not HL\overline{H L}.

STEP 6

d. JKKJ\overline{J K} \cong \overline{K J}This statement is true because KJ\overline{K J} is the same line as JK\overline{J K}, just in the opposite direction. Therefore, they are congruent.

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