Question

select the correct answer
given statements:
if a shape is a parallelogram, then the shape has opposite angles congruent.
a rhombus is a parallelogram.
what is a logical conclusion from the given statements?
a. a parallelogram is a rhombus
b. a rhombus has opposite sides congruent
c. a parallelogram has opposite sides congruent
d. a rhombus has opposite angles congruent
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Explanation:

We have two statements: 1) If a shape is a parallelogram, then the shape has opposite angles congruent. 2) A rhombus is a parallelogram. By the law of syllogism (or transitive property of implications), we can conclude that since a rhombus is a parallelogram and parallelograms have opposite angles congruent, a rhombus has opposite angles congruent. Let's analyze each option:

• Option A: Not all parallelograms are rhombuses (a rhombus has all sides equal, a parallelogram just needs opposite sides equal), so this is incorrect.
• Option B: While a rhombus does have opposite sides congruent (since it's a parallelogram), this is not the conclusion derived from the given statements. The given statements lead us to the angle congruence property for rhombus, not the side congruence (though side congruence is true, it's not the logical conclusion from the provided implications).
• Option C: This is a property of parallelograms, but we need a conclusion about rhombus from the given statements (that connect parallelogram to angle congruence and rhombus to parallelogram), so this is not the right conclusion here.
• Option D: Since a rhombus is a parallelogram (second statement) and parallelograms have opposite angles congruent (first statement), by modus ponens (or transitivity), we can conclude a rhombus has opposite angles congruent. This follows the logical flow of the given statements.

Answer:

D. A rhombus has opposite angles congruent