What are the theorems of a parallelogram?

Theorems on Parallelograms

• Theorem1: A diagonal of a parallelogram divides it into two congruent triangles.
• Theorem 2: In a parallelogram, opposite sides are equal.
• Theorem 3: In a parallelogram, opposite angles are equal.
• Theorem 4: The diagonals of a parallelogram bisect each other.
• Q.

How many theorems are there in parallelogram?

You have now proven two theorems about parallelograms. You can use these theorems in future proofs without proving them again. Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles. Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent.

What are the 7 properties of a parallelogram?

Properties of Parallelograms Explained

• Opposite sides are parallel. …
• Opposite sides are congruent. …
• Opposite angles are congruent. …
• Same-Side interior angles (consecutive angles) are supplementary. …
• Each diagonal of a parallelogram separates it into two congruent triangles. …
• The diagonals of a parallelogram bisect each other.

What are the 5 theorems?

Thus the five theorems of congruent triangles are SSS, SAS, AAS, HL, and ASA.

• SSS – side, side, and side. …
• SAS – side, angle, and side. …
• ASA – angle, side, and angle. …
• AAS – angle, angle, and side. …
• HL – hypotenuse and leg.

What are the 4 properties of parallelograms?

Properties of parallelograms

• 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.

How do you find the theorem of a parallelogram?

Video quote: Cut by this red transversal and that makes the two consecutive interior angles supplementary easy as that. So we could all get x and y or those two angles at P and Q.

How do you solve the different theorems of a parallelogram?

Four important theorems related to the properties of a parallelogram are given below: Opposite sides of a parallelogram are equal. Opposite angles of a parallelogram are equal. Diagonals of a parallelogram bisect each other.

1. AC = AC (Common sides)
2. AB = CD (since alternate interior angles are equal)
3. AD = BC (given).

What are the 8 properties of a parallelogram?

Properties of Parallelogram



The opposite sides are parallel and congruent. The opposite angles are congruent. The consecutive angles are supplementary. If any one of the angles is a right angle, then all the other angles will be at right angle.

What theorems state how do you prove a parallelogram by its sides?

1. Opposite Sides Theorem Converse: If both pairs of opposite sides of a quadrilateral are congruent, then the figure is a parallelogram. 2. Opposite Angles Theorem Converse: If both pairs of opposite angles of a quadrilateral are congruent, then the figure is a parallelogram.

What is the midline theorem?

The midline theorem is a triangle theorem that states that the line segment that joins two midpoints of a triangle will be parallel to the third side and the length of the midsegment will be equal to half the length of the third side.

What is similarity theorem?

The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle’s third side.

What is the triangle Midsegment theorem?

Midsegment Theorem: The segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

What are the theorems of trapezoid?

Theorem: The base angles of an isosceles trapezoid are congruent. The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.



Writing a Two-Column Proof.

What is theorems or trapezoid and kite?

THEOREM: If a quadrilateral is an isosceles trapezoid, the opposite angles are supplementary. THEOREM: (converse) If a trapezoid has its opposite angles supplementary, it is an isosceles trapezoid. A kite is a quadrilateral whose four sides are drawn such that there are two distinct sets of adjacent, congruent sides.

What are the theorems of a kite?

In kite, adjacent sides are equal and long diagonal bisect the small diagonal at right angle. All interior angles are acute angles. Theorem 1 : If a quadrilateral is a kite, then its diagonals are perpendicular. 6) ΔABD is an Isosceles triangle.

What is the theorem of rhombus?

The opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each vertex angle. The diagonals of a rhombus bisect each other at right angles.

Which theorem can you use to show that the quadrilateral is a parallelogram?

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 both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

What is the theorem of rectangle?

Theorems. The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter, the square has the largest area. The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle. A parallelogram with equal diagonals is a rectangle.

What theorem or postulate is used to prove ABCD is a parallelogram?

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

What are the 5 ways to prove a figure is a parallelogram?

How To Prove a Parallelogram? 17 Step-by-Step Examples For Mastery!

• Both pairs of opposite sides are parallel.
• Both pairs of opposite sides are congruent.
• Both pairs of opposite angles are congruent.
• Diagonals bisect each other.
• One angle is supplementary to both consecutive angles (same-side interior)

Which of the following is not true for a parallelogram?

Correct Answer: Option (C) Opposite angles are bisected by the diagonals. In a parallelogram, opposite angles are not bisected by the diagonals. To learn more Maths related questions and answers, visit BYJU’S – The Learning App.

What is a parallelogram with four right angles and four congruent sides?

A square is one of the most basic geometric shapes. It is a special case of a parallelogram that has four congruent sides and four right angles. A square is also a rectangle because it has two sets of parallel sides and four right angles. A square is also a parallelogram because its opposite sides are parallel.

What is a parallelogram with 4 equal sides?

A rhombus is a parallelogram with all four sides congruent to each other. diamond-like shape. A square is a parallelogram with four congruent sides and four right angles. In other words, a square is a rectangle and a rhombus.

Do parallelograms have 4 congruent sides?

A square is a parallelogram. This is always true. 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.

What type of parallelogram has 4 congruent angles?

A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Do all parallelograms have 4 right angles?

Right Angles in Parallelograms



In a parallelogram, if one of the angles is a right angle, all four angles must be right angles. If a four-sided figure has one right angle and at least one angle of a different measure, it is not a parallelogram; it is a trapezoid.

Do all quadrilaterals have four sides and four angles yes or no?

Every quadrilateral has 4 sides, 4 vertices, and 4 angles. 4. The total measure of all the four interior angles of a quadrilateral is always equal to 360 degrees. The sum of interior angles of a quadrilateral fits the formula of polygon i.e.