Handwritten Notes

What are the properties of the opposite angles in a rhombus?

In a rhombus, opposite angles are congruent. This means that each pair of opposite angles has the same measure.

What is the relationship between adjacent angles in a parallelogram?

Adjacent angles in a parallelogram are supplementary, meaning that their measures add up to 180 degrees.

How can you determine if a quadrilateral is a parallelogram based on its angles?

For a quadrilateral to be classified as a parallelogram, both pairs of opposite angles must be congruent. If one pair of opposite angles is congruent, the quadrilateral is a parallelogram.

What is the sum of the measures of the angles in any quadrilateral?

The sum of the measures of the angles in any quadrilateral is always 360 degrees.

What must be true about the sides of a rectangle?

In a rectangle, opposite sides are always congruent, and all angles are right angles (90 degrees).

What is the relationship between the diagonals of a rectangle?

The diagonals of a rectangle are congruent and bisect each other.

What is the area of a rectangle that is 4 times as long as it is wide and has an area of 6400 sq cm?

If a rectangle's area is 6400 sq cm and it is 4 times as long as it is wide, the width is 40 cm and the length is 160 cm.

What is the classification of a quadrilateral with one angle measuring 65° and two adjacent angles measuring 120° and 125°?

This quadrilateral is not a parallelogram because it has an adjacent pair of supplementary angles, which violates the properties of parallelograms.

What is the value of m∠LIM if m∠LIM + m∠M + 27 = 180?

To find m∠LIM, you would solve the equation m∠LIM + 56 + 27 = 180, resulting in m∠LIM = 97°.

What is the relationship between the sides of a rhombus?

In a rhombus, all four sides are congruent, meaning they are all of equal length.

What must m∠BCD be for quadrilateral ABCD to be a parallelogram?

For ABCD to be a parallelogram, m∠BCD must be equal to m∠DAB, ensuring that opposite angles are congruent.

What is the sum of the diagonals of a rectangle with an area of 6400 sq cm?

The sum of the diagonals of a rectangle can be calculated using the Pythagorean theorem. For a rectangle with length 160 cm and width 40 cm, the sum of the diagonals is approximately 329.8 cm.

What is true about the diagonals of a parallelogram?

The diagonals of a parallelogram bisect each other, meaning they cut each other in half at their intersection point.

What is the classification of a trapezoid with one pair of parallel sides?

A trapezoid is classified as an isosceles trapezoid if the non-parallel sides are congruent.

What is the relationship between the angles in a rectangle?

In a rectangle, all angles are right angles, and opposite angles are congruent.

What is the value of x if KR = x + 7, KM = 3x - 5, and JL = 4x - 10?

To find x, you would set up the equation based on the relationships given. Solving yields x = 19.

What is the measure of angle ZABC if it is given as 71°?

If m∠ZABC is given as 71°, then that is the measure of the angle in question.

What is the relationship between the sides of a trapezoid?

In a trapezoid, only one pair of opposite sides is parallel, while the other pair may or may not be congruent.

What is the measure of angle DZW in parallelogram WXYZ if x = 14?

If x = 14, then m∠DZW can be calculated based on the properties of the parallelogram, resulting in m∠DZW = 112°.

What is the relationship between the angles in a rhombus?

In a rhombus, opposite angles are congruent, and adjacent angles are supplementary.