**If both pairs of opposite sides of a quadrilateral are congruent**, then the quadrilateral is a parallelogram. If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. … If ∠A ≅ ∠C and ∠B ≅ ∠D, then ABCD is a parallelogram.

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**negative impact of internet on democracy**.

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MATH is a rectangle because it is a parallelogram with a right angle. 10 ANS: To prove that ABCD is a parallelogram, show that **both pairs of opposite sides of the parallelogram are parallel by showing the opposite sides have the same slope**: A rectangle has four right angles.

Statements | Reasons |
---|---|

Definition of Rectangle | |

ΔBCD ≅ ΔADC | Side, Angle, Side |

AC ≅ BD | CPCTC |

DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. THEOREM: **If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram**. THEOREM: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram.

Figure ABCD is a parallelogram. What is the perimeter of ABCD? What is the perimeter of parallelogram LMNO? The perimeter of parallelogram ABCD is **46** inches.

Figure ABCD is a parallelogram. The value of n is **17**.

9.3. II. A parallelogram : In a quadrilateral, **if both pairs of opposite sides are parallel and equal**, then it is called a parallelogram. i.e., AB || CD and AB = CD; AD || BC and AD = BC, then ABCD is a parallelogram.

Since each pair of opposite sides of the quadrilateral have the same measure, they are congruent. Quadrilateral ABCD is a **parallelogram**. The length of each diagonal is 130. Since the diagonals are congruent, ABCD is a rectangle by Theorem 6.14.

- It has two pairs of parallel opposite sides.
- It has two pairs of equal opposite angles.
- It has two pairs of equal and parallel opposite sides.
- Its diagonals bisect each other.

By the transitive property of ~=, you have **all four angles congruent**. Because the measures of the interior angles of a quadrilateral add up to 360, you can show that all four angles of our parallelogram are right angles. That’s more than enough to make your parallelogram a rectangle.

In a parallelogram, opposite sides will be parallel, by proving that slope of opposite sides are equal, we may say that opposite sides are parallel. So, the given points form a parallelogram. Example 2 : If the points A(2, 2), B(–2, –3), C(1, –3) and D(x, y) form a parallelogram then find the value of x and y.

- Opposite sides are congruent (AB = DC).
- Opposite angels are congruent (D = B).
- Consecutive angles are supplementary (A + D = 180°).
- If one angle is right, then all angles are right.
- The diagonals of a parallelogram bisect each other.

**If both pairs of opposite angles of a quadrilateral are congruent**, then it’s a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

Which statement proves that △XYZ is an isosceles right triangle? **The slope of XZ is 3/4, the slope of XY is -4/3, and XZ = XY = 5.**

To find the perimeter of triangle ABC we use the Pythagorean Theorem which tells us that |AB|^2 = |AC|^2 + |BC|^2. Since |AC| = 5 and |BC| = 12 we find that |AB| = sqrt{169} = 13. The perimeter of triangle ABC is then **5 + 12 + 13 = 30 units**.

Figure ABCD is a **parallelogram**.

Which concept can be used to prove that the diagonals of a parallelogram **bisect** each other? A)Congruent Triangles. You just studied 20 terms!

If we add all three angles in any triangle we get 180 degrees. So, the measure of angle A **+ angle B + angle C = 180 degrees**.

Answer: Let A, B, C, D be the four sides; then if the vectors are oriented as shown in the figure below we **have A + B = C + D**. Thus two opposite sides are equal and parallel, which shows the figure is a parallelogram.

1)The diagonals are congruent.4)The opposite sides are parallel.

If a parallelogram is known to have one right angle, then **repeated use of co-interior angles** proves that all its angles are right angles. If one angle of a parallelogram is a right angle, then it is a rectangle.

1) Show **that all angles are 90 degrees**. 2) Show that one set of sides is parallel ,and that two opposite angles are 90 degrees. 3) Show that the diagonals bisect each other, and that they are equal in length. 4) Show that it is a parallelogram and that diagonals are equal in length.

- Opposite sides are congruent (AB = DC).
- Opposite angels are congruent (D = B).
- Consecutive angles are supplementary (A + D = 180°).
- If one angle is right, then all angles are right.
- The diagonals of a parallelogram bisect each other.

- Prove that opposite sides are congruent.
- Prove that opposite angles are congruent.
- Prove that opposite sides are parallel.
- Prove that consecutive angles are supplementary (adding to 180°)
- Prove that an angle is supplementary to both its consecutive angles.

- If all angles in a quadrilateral are right angles, then it’s a rectangle (reverse of the rectangle definition). …
- If the diagonals of a parallelogram are congruent, then it’s a rectangle (neither the reverse of the definition nor the converse of a property).

Every quadrilateral has parallel sides. … Every rectangle has perpendicular sides. **True**. **Every rectangle is a parallelogram**.

We also know that if the opposite sides have equal side lengths, then ABCD is a parallelogram. Here, since the lengths of the opposite sides are equal that is: [AB = CD = 8]units and [BC = DA = sqrt {41} ]units. Hence, the given vertices are the vertices of a parallelogram.

Examine whether the given points A (4, 6) and B (7, 7) and C (10, 10) and D (7, 9) forms a parallelogram. Length of opposite sides are equal. So the given vertices forms a parallelogram. Since the midpoint of diagonals are equal, the given points form a parallelogram.

If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. **If both pairs of opposite angles of a quadrilateral are congruent**, then the quadrilateral is a parallelogram.

how can cassius prove that quadrilateral abcd is a parallelogram? XXX since ae ≅ ce and be ≅ de then e is the midpoint of ac and bd. cassius can use that **to show that ac and bd are congruent**, and thus quadrilateral abcd is a parallelogram. shizuku was asked to prove that the diagonals of wxyz bisect each other.

which plan should you use to prove that an angle of abcd is supplementary to both of its consecutive angles? use **m∠a= 104 and m∠b = 76 to** show that ∠a and ∠b are same-side interior angles. then, use ab∥cd to show that ∠a and ∠d are supplementary angles.