That is, if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem: The diagonals of a parallelogram bisect each other.
How do you know if diagonals bisect each other?
In any parallelogram, the diagonals (lines linking opposite corners) bisect each other. That is, each diagonal cuts the other into two equal parts.
How do you know if a diagonal is perpendicular?
To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem – If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
What is the diagonal of rhombus perpendicular?
Proof that the diagonals of a rhombus are perpendicular
Corresponding parts of congruent triangles are congruent, so all 4 angles (the ones in the middle) are congruent. This leads to the fact that they are all equal to 90 degrees, and the diagonals are perpendicular to each other.
How do you know if a slope is perpendicular to a diagonal?
Correct answer:
Explanation: If the slopes of two lines can be calculated, an easy way to determine whether they are perpendicular is to multiply their slopes. If the product of the slopes is , then the lines are perpendicular. In this case, the slope of the line is and the slope of the line is .
Are diagonals perpendicular in a kite?
Proof: The diagonals of a kite are perpendicular.
How do you prove that the diagonals of a parallelogram are perpendicular?
= A · A – B · B. Therefore, (A + B) · (A – B)=0 ⇔ A · A = B · B. I.e., the diagonals are perpendicular if and only if two adjacent edges have equal lengths. In other words, if the parallelogram is a rhombus.
Are the diagonals of a parallelogram equal?
Are the Diagonals of a Parallelogram Equal? The diagonals of a parallelogram are NOT equal. The opposite sides and opposite angles of a parallelogram are equal.
Are diagonals always perpendicular in a parallelogram?
The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.