图形 X 是一个梯形,图形 Y 是一个平行四边形。下列哪一对陈述是正确的?

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完整解法

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1. Evaluate Option (1)

Option (1) states that Figure X has opposite sides that are parallel. Figure X is a trapezium, which has only one pair of parallel sides (top and bottom), not both pairs. Figure Y is a parallelogram, which does have opposite sides parallel. Since the statement for Figure X is false, Option (1) is false.

2. Evaluate Option (2)

Option (2) states that Figure X has one pair of perpendicular lines. Figure X has a vertical left side and a horizontal bottom side, meeting at ∠b\angle b, which is marked with a right angle. Thus, it has one pair of perpendicular lines. It also states Figure Y does not have any pair of perpendicular lines. Figure Y is a slanted parallelogram with no right angles. Both statements are true, so Option (2) is true.

3. Evaluate Option (3)

Option (3) states ∠c+∠d=180∘\angle c + \angle d = 180^\circ for Figure X. Since the top and bottom sides are parallel, the interior angles on the same side of the transversal sum to 180∘180^\circ, so ∠c+∠d=180∘\angle c + \angle d = 180^\circ is true. For Figure Y, it states ∠f+∠h=180∘\angle f + \angle h = 180^\circ. ∠f\angle f and ∠h\angle h are opposite angles in a parallelogram, so they are equal, not supplementary (unless it's a rectangle, which it isn't). Thus, Option (3) is false.

4. Evaluate Option (4)

Option (4) states ∠a+∠b=180∘\angle a + \angle b = 180^\circ for Figure X. This is true as they are interior angles between parallel lines. For Figure Y, it states ∠e+∠h=180∘\angle e + \angle h = 180^\circ. ∠e\angle e and ∠h\angle h are adjacent angles on the bottom side, which do not sum to 180∘180^\circ (they are not interior angles between parallel lines; rather, ∠e+∠f=180∘\angle e + \angle f = 180^\circ or ∠e+∠g=180∘\angle e + \angle g = 180^\circ if gg is adjacent). Thus, Option (4) is false.

答案

Option (2)

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