Table of Contents

## Which angle pair are bisected by a diagonal?

The diagonals of a rhombus bisect each other at right angles.

## Does the diagonals of square bisect the angles?

A square is a special case of an isosceles trapezoid, kite, parallelogram, quadrilateral, rectangle, rhombus, and trapezoid. The diagonals of a square bisect one another and are perpendicular (illustrated in red in the figure above). In addition, they bisect each pair of opposite angles (illustrated in blue).

**How many triangles are formed by a diagonal of a parallelogram?**

two congruent triangles

Theorem 15.5: A diagonal of a parallelogram separates it into two congruent triangles.

### Does diagonal of parallelogram bisect the angle?

A parallelogram is a quadrilateral whose opposite sides are parallel. The opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are equal. The diagonals of a parallelogram bisect each other.

### What are the diagonal properties of a parallelogram?

The diagonals bisect each other. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent triangles.

**How do you verify that the diagonals bisect each other?**

Expert Answer:

- ABCD is a parallelogram, diagonals AC and BD intersect at O.
- In triangles AOD and COB,
- DAO = BCO (alternate interior angles)
- AD = CB.
- ADO = CBO (alternate interior angles)
- AOD COB (ASA)
- Hence, AO = CO and OD = OB (c.p.c.t)
- Thus, the diagonals of a parallelogram bisect each other.

#### How do 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.

#### What does it mean for diagonals to bisect opposite angles?

**Do the diagonals of a square bisect each other perpendicularly?**

The diagonals of a square are perpendicular bisectors of one another. As a result, Their intersection forms four right angles, and each diagonal is split into two congruent pieces.

## What is formed if a diagonal is drawn in a parallelogram?

Diagonals in Parallelograms A diagonal acts as a transversal and creates alternate interior angles with the parallel sides. When both diagonals are drawn, two pairs of congruent vertical angles are formed. When one diagonal is drawn in a parallelogram, two congruent triangles are formed.

## What triangles are formed by a diagonal of a square?

Each diagonal divides the square into two congruent isosceles right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the square.

**How do you prove that the diagonals bisect the angles?**

In a rhombus ABCD, prove that the diagonals bisect the angles. i.e prove that ∠BAC ≅ ∠DAC and that ∠BCA ≅ ∠DCA; and also that ∠ADB ≅ ∠CDB and ∠ABD ≅ ∠CBD Wow, that’s a lot of angles and a lot of triangles! Fortunately, we know so much about the sides, as we are dealing with a rhombus, where all the sides are equal.

### What is the Pythagoras theorem?

The theorem is named after a greek Mathematician called Pythagoras. “c” is the hypotenuse. According to the definition, the Pythagoras Theorem formula is given as: The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.

### Do the diagonals bisect the angles of a rhombus ABCD?

Since it is symmetrical, the diagonals bisect the angles, as we will show using triangle congruence. In a rhombus ABCD, prove that the diagonals bisect the angles. i.e prove that ∠BAC ≅ ∠DAC and that ∠BCA ≅ ∠DCA; and also that ∠ADB ≅ ∠CDB and ∠ABD ≅ ∠CBD

**How do you use the Pythagorean theorem to solve 3-dimensional problems?**

Pythagoras’ theorem can be applied to solve 3-dimensional problems. The longest side of a right-angled triangle is the hypotenuse. The hypotenuse is always opposite the right angle. Draw a square on each side of a right-angled triangle. Calculate the area of each square.