How do you prove that the diagonals of a parallelogram bisect each other?

Expert Answer:
  1. ABCD is a parallelogram, diagonals AC and BD intersect at O.
  2. In triangles AOD and COB,
  3. DAO = BCO (alternate interior angles)
  4. AD = CB.
  5. ADO = CBO (alternate interior angles)
  6. AOD COB (ASA)
  7. Hence, AO = CO and OD = OB (c.p.c.t)
  8. Thus, the diagonals of a parallelogram bisect each other.

Are the diagonals of a parallelogram congruent?

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. A square is always a rhombus.

How do you prove if the diagonals of a parallelogram are congruent then the parallelogram is a rectangle?

If the diagonals of a parallelogram are congruent (=equal), then the parallelogram is a rectangle. Proof: opposite sides of a parallelogram are equal, so that if the diagonals are equal as well, then triangles ABC and BAD are congruent, as AB=BA, BC=AD and AC=BD. So angles ABC and BAD are equal.

How do you prove that the diagonals of a parallelogram are perpendicular?

Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e., its four sides have equal lengths. (A + B) · (A – B) = A · A – B · B. Therefore, (A + B) · (A – B)=0 ⇔ A · A = B · B.

What is congruent in a parallelogram?

It is a quadrilateral where both pairs of opposite sides are parallel. There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). Opposite angels are congruent (D = B). Consecutive angles are supplementary (A + D = 180°).

How do you find diagonals of a parallelogram?

Explanation: In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for . \displaystyle 20 – 3x = 2x – 4 \rightarrow 24 = 5x \rightarrow 4.8 = x. Then, substitute 4.8 for in each labeled segment to get a total of 11.2 for the diagonal length.

How do you prove that two lines are perpendicular in a parallelogram?

If the two lines intersect at a point, the vertical angles formed are congruent. The intersecting lines either form a pair of acute angles and a pair of obtuse angles, or the intersecting lines form four right angles. When the lines meet to form four right angles, the lines are perpendicular.

What is true about the diagonals of a parallelogram?

The diagonals of a parallelogram 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.

Are diagonals of a parallelogram perpendicular?

If a parallelogram is a rhombus, then its diagonals are perpendicular. If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

What is the formula for diagonal?

The formula to calculate the number of diagonal of an n-sided polygon = n(n-3)/2 where n is the number of sides of the polygon.

Which statement is always true the diagonals of a parallelogram are congruent?

The diagonals are perpendicular. The diagonals bisect their respective angles. 7 Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?
…
1) and bisect each other.
4) and

What are congruent diagonals?

Properties of a square

The diagonals are congruent. The diagonals are perpendicular to and bisect each other. A square is a special type of parallelogram whose all angles and sides are equal. Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.

Which statement about parallelogram is always true?

Two pairs of opposite sides are congruent. The diagonals are perpendicular to each other. 4 In parallelogram QRST, diagonal is drawn. Which statement must always be true?
…
1) The diagonals are congruent.
3) The opposite angles are congruent.
4) The opposite sides are parallel.

Which of the following statements are always true of parallelograms quizlet?

Which of the following statements are always true of parallelograms? It is a quadrilateral, Both pairs of opposite sides are parallel.. If a diagonal is drawn in a parallelogram, then two congruent triangles are formed.

Which statement is always true about the opposite angles of a parallelogram?

Sal proves that opposite angles of a parallelogram are congruent.

Which statements are true about parallelograms select three options?

The parallelogram has the following properties:
  • Opposite sides are parallel by definition.
  • Opposite sides are congruent.
  • Opposite angles are congruent.
  • Consecutive angles are supplementary.
  • The diagonals bisect each other.

Which statement is true about a parallelogram that has 4 right angles and 4 equal side lengths?

Squares
This is always true. Â Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

Which statement is always true for parallelograms Quizizz?

Which statement is always true for parallelograms? Samantha states that a parallelogram is always a rhombus. Is she correct? Yes, because a parallelogram has opposite angles that are equal in size.

Which of the following apply to all parallelograms?

Parallelogram properties apply to rectangles, rhombi and squares. In a parallelogram, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and diagonals bisect each other. Other important polygon properties to know are trapezoid properties, and kite properties.

Do all parallelograms have 4 equal angles?

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
…
Parallelogram
This parallelogram is a rhomboid as it has no right angles and unequal sides.
Type quadrilateral, trapezium
Edges and vertices 4
Symmetry group C2, [2]+,

Does parallelogram have 4 right angles?

Parallelogram: A quadrilateral with 2 pairs of parallel sides. Rectangle: A parallelogram with 4 right angles.

Does a parallelogram have to have 4 equal sides?

Rectangles, squares and rhombuses are all classified as parallelograms. The classic parallelogram looks like a slanted rectangle, but any four-sided figure that has parallel and congruent pairs of sides can be classified as a parallelogram.

Are diagonals of a rectangle congruent?

The rectangle has the following properties:

All angles are right angles by definition. The diagonals are congruent.