FAQs
Solution: Given: The diagonal AC of a parallelogram ABCD bisects ∠A. We can use alternate interior angles property to show that the diagonal AC bisects ∠C and by showing all sides are equal, it can be proved ABCD is a rhombus.
How do you prove that ABCD is a rhombus? ›
In geometry, a rhombus is a quadrilateral that has all equal sides, with opposite sides parallel to each other. The quadrilateral ABCD is a rhombus, with AB = BC = CD = AD. AB is parallel to CD (AB||CD), and BC is parallel to AD (BC||CD).
When the diagonals of a parallelogram bisect each other then it must be a rhombus response? ›
Answer and Explanation: A rhombus is a parallelogram with four congruent sides. However, this questions is asking us about diagonals. A parallelogram will be a rhombus if its diagonals bisect pairs of opposite angles, but not each other, making choice 2 wrong.
What are the diagonals of a quadrilateral ABCD bisect each other if A is 45 then B? ›
∠A=45∘But ∠A+∠B=180∘ (Sum of consecutive angles)∴∠B=180∘−∠A=180∘−45∘=135∘
Do diagonals bisect in a rhombus? ›
The diagonals of a rhombus bisect each other at right angles.
How do you prove ABCD ABCD 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.
How to prove a parallelogram? ›
There are five ways to prove that a quadrilateral is a parallelogram:
- Prove that both pairs of opposite sides are congruent.
- Prove that both pairs of opposite sides are parallel.
- Prove that one pair of opposite sides is both congruent and parallel.
- Prove that the diagonals of the quadrilateral bisect each other.
What formula do you use to prove a rhombus? ›
Say that the rectangle had side lengths of length e and f. Then the side lengths of quadrilateral ABCD, by the Pythagorean Theorem, are √(e2)2+(f2)2. Since all sides of this quadrilateral are equal then quadrilateral ABCD must be a rhombus.
What happens when the diagonals of a parallelogram bisect each other? ›
The diagonal lines of a parallelogram will bisect each other at the midpoint of each line. This means that each line will be cut in half by the other line.
What is the diagonal theorem of a parallelogram? ›
The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram bisects it into two congruent triangles. If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.
In a special parallelogram as square, rhombus etc. diagonals bisect each other at right angle but in general parallelogram, diagonals of a parallelogram only bisects each other.
What if the diagonals bisect each other in a quadrilateral? ›
2. If the Diagonals of a quadrilateral bisect each other,it is a parallelogram.
Is ABCD a rhombus? ›
In a rhombus ABCD show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. ABCD is a rhombus.
What if the diagonals of a quadrilateral are equal and bisect each other? ›
If the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
What is the formula for the diagonal AC? ›
Length of Diagonals
Length of Diagonal | Formulas |
---|
Length of diagonal of Square | a√2 where a is the length of the side of the square |
Length of diagonal of Rectangle | √(l2 + b2) Where l and b are the length and breadth of the rectangle, respectively |
Length of diagonal of Cube | a√3 Where a is the length of edges of the cube |
1 more row
Is ABCD a rectangle in which AC bisects A and C? ›
Summary: If ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C, we have proved that ABCD is a square and diagonal BD bisects ∠B as well as ∠D.
Do the diagonals of a parallelogram ___________________ bisect each other? ›
Answer: The statement "The diagonals of a parallelogram bisect each other" is true. A parallelogram is a four-sided figure with opposite sides that are parallel. The diagonals of a parallelogram are the line segments that connect opposite corners of the parallelogram.
What if the diagonals of a parallelogram ABCD are equal? ›
In a parallelogram if two diagonals are equal, then the parallelogram is a rectangle.So, ABCD is a rectangle.It is known that each interior angle of a rectangle is 90 degree. Since ABC is an interior angle of rectangle ABCD, so measure of angle ABC is 90 degree. Q.