Which statement is always true about a parallelogram?
A. It has 4 congruent sides
B. It has 4 right angles.
C. It has opposite angles that are congruent.
D. The sum of any 3 angles is 360
Is it a?
hmm,, recall that when we consider a parallelogram, we also consider square, rhombus, and rectangle (they are all parallelogram)
now, let's analyze each choices:
for (a), it's only true for a square.
for (b), it's true for square and rectangle.
for (c), it's true for any parallelogram
for (d), it's wrong, since sum of all four angles must be 360.
thus the answer is (c).
hope this helps~ :)
Properties of Parallelogram:
Opposite sides of a parallelogram are parallel and so will never intersect.
Opposite sides of a parallelogram are equal in length.
Opposite angles of a parallelogram are equal in measure.
Adjacent angles are supplementary (add up to 180°).
The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
The diagonals of a parallelogram bisect each other.
Any line through the midpoint of a parallelogram bisects the area.
The perimeter of a parallelogram is 2(a + b) where a and b are the lengths of adjacent sides.
The sum of the squares of the sides equals the sum of the squares of the diagonals.
No, statement A is not always true about a parallelogram. A parallelogram may have two pairs of congruent sides, but it is not required for all four sides to be congruent.
To determine the correct answer, we can use our knowledge of the properties of a parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Based on these properties, we can evaluate the statements:
B. It has 4 right angles - This statement is false. A parallelogram does not always have right angles unless it is a rectangle (a specific type of parallelogram).
C. It has opposite angles that are congruent - This statement is true. Opposite angles in a parallelogram are congruent. This property holds for all parallelograms.
D. The sum of any 3 angles is 360 - This statement is false. The sum of the interior angles of a parallelogram is always 360 degrees, but this statement refers to the sum of any three angles. Since a parallelogram has four angles, the sum of any three angles will be less than 360 degrees.
Therefore, the correct answer is C. It is always true that a parallelogram has opposite angles that are congruent.