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Answer :
In parallelogram WXYZ, the shorter sides are 12 inches, and the longer sides are 24 inches. The true statements are that (B) opposite sides are parallel, (C) opposite angles are congruent, and (F) if one angle is 120 degrees, then the (G) opposite angle is also 120 degrees while the other two are 60 degrees each.
Let's analyze the properties of parallelogram WXYZ based on the given information. Since WX and ZY are 12 inches each, and the shorter sides are half the length of the longer sides, XY and WZ must be 24 inches each.
We are given that angle Y is 120 degrees, and in a parallelogram, opposite angles are congruent. Thus, angle W is also 120 degrees. Since the sum of the angles in any quadrilateral is 360 degrees, angles X and Z are each 60 degrees (360 - 2*120 = 120, and 120/2 = 60).
A. The statement that quadrilateral WXYZ is a rectangle is false because not all angles are 90 degrees.
B. The statement that the quadrilateral has opposite sides that are parallel is true, which is a fundamental property of parallelograms.
C. The statement that the quadrilateral has opposite angles that are congruent is true, since angle Y is equal to angle W (120 degrees), and angle X is equal to angle Z (60 degrees).
D. The statement that if WX = 12 in., then XY = 6 in. is false, because the longer sides (XY and WZ) should actually be 24 inches each.
E. The statement that side WZ must be 12 inches is false, as WZ is 24 inches.
F. The statement that the measure of angle Z is equal to the measure of angle X is true, both are 60 degrees.
G. The statement that the measure of angle W is 120 degrees is true.
H. The statement that the measure of angle Z is 120 degrees is false; angle Z is 60 degrees.
Hence, the correct options are B,C,F and G
Complete Question:-
In parallelogram WXYZ, the shorter sides are half the length of the longer sides.
Parallelogram W X Y Z. The length of sides W X and Z Y are 12 inches. Angle Y is 120 degrees. Angle Y is opposite to Angle W.
Which statements are true? CHECK ALL THAT APPLY.
A. Quadrilateral WXYZ is a rectangle.
B. The quadrilateral has opposite sides that are parallel.
C. The quadrilateral has opposite angles that are congruent.
D. If W X = 12 in., then X Y = 6 in.
E. Side WZ must be 12 inches.
F. mAngle Z = measure of angle X
G. Measure of angle W = 120 degrees
H. Measure of angle Z = 120 degrees
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Rewritten by : Barada
In parallelogram WXYZ, opposite sides are parallel, and opposite angles are congruent, which confirms a few of the statements provided. However, the claim that WXYZ is a rectangle is incorrect due to the given angle measures.
Given that parallelogram WXYZ has sides WX and ZY equal to 12 inches and angle Y is 120 degrees, we can analyze the properties and verify which statements are true:
- Quadrilateral WXYZ is a rectangle. This statement is false since a rectangle requires all angles to be 90 degrees, but angle Y is 120 degrees.
- The quadrilateral has opposite sides that are parallel. This statement is true because opposite sides in a parallelogram are always parallel.
- The quadrilateral has opposite angles that are congruent. This statement is true because opposite angles in a parallelogram are always equal.
- If WX = 12 in., then XY = 6 in. This statement is false because WX and XY are sides of a parallelogram, not related such that one is half the other unless specified differently.
- Side WZ must be 12 inches. This statement is false because WZ would be the same length as XY, not necessarily 12 inches.
- m∠Z = m∠X. This statement is true because opposite angles in a parallelogram are equal.
- Measure of angle W = 120 degrees. This statement is false because angle W, being adjacent to angle Y, would be supplementary to 120 degrees, making it 60 degrees.
- Measure of angle Z = 120 degrees. This statement is false because angle Z and angle Y being opposite angles would be equal, making angle Z also 120 degrees.
