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QuestionQuadrilaterals ABCDABCD and HJKLHJKL are congruent. Find which angles are congruent: ∠K≅\angle K \cong (A, D, C, or L).

Studdy Solution

STEP 1

Assumptions1. Quadrilateral ABC is congruent to Quadrilateral HJK. . This means that corresponding sides and angles of the two quadrilaterals are equal.
3. We are asked to find which angle in Quadrilateral ABC is congruent to angle K in Quadrilateral HJK.

STEP 2

In congruent figures, corresponding parts are equal. So, we need to identify the corresponding angle to angle K in Quadrilateral ABC.

STEP 3

Since the quadrilaterals are congruent and we are given that the order of vertices in Quadrilateral ABC corresponds to the order of vertices in Quadrilateral HJK, we can say that angle K in Quadrilateral HJK corresponds to angle B in Quadrilateral ABC.

STEP 4

Therefore, we have the following congruence statement∠K≅∠B\angle K \cong \angle B

STEP 5

Now, let's check the given optionsa. ∠K≅∠A\angle K \cong \angle A - This is incorrect because angle K corresponds to angle B, not angle A.
b. ∠K≅∠D\angle K \cong \angle D - This is incorrect because angle K corresponds to angle B, not angle D.
c. ∠K≅∠C\angle K \cong \angle C - This is incorrect because angle K corresponds to angle B, not angle C.
d. ∠K≅∠L\angle K \cong \angle L - This is incorrect because angle K and angle L are in the same quadrilateral and cannot be congruent unless it's a special quadrilateral like a rectangle or square, which is not mentioned in the problem.
So, none of the given options are correct. The correct congruence statement is ∠K≅∠B\angle K \cong \angle B.

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