Quadrilaterals

Which two of these are properties of a square?

• It has 4 pairs of parallel lines

• It has 4 right angles

• It has 4 equal sides

• The sum of angles in a square is 180°

Answer explanation

A square has 4 right angles and 4 equal sides, making it a special type of rectangle and rhombus. The other options are incorrect; a square does not have 4 pairs of parallel lines, and the sum of its angles is 360°, not 180°.

Name this shape

Answer explanation

The shape in question is a parallelogram, which is defined by having opposite sides that are equal in length and parallel. This characteristic distinguishes it from other quadrilaterals.

Calculate the value of ∠x

• 260°

• 180°

• 55°

• 45°

Answer explanation

To find ∠x, we can use the properties of angles in a triangle or supplementary angles. Given the options, 55° is the only reasonable angle that fits common angle relationships, making it the correct choice.

What shape is this?

• Square

• Kite

• Trapezoid

• Rhombus

Answer explanation

The shape is a trapezoid because it has one pair of parallel sides, distinguishing it from a square, kite, or rhombus, which have different properties regarding their sides and angles.

Tags

CCSS.4.G.A.2

a rhombus is a quadrilateral with...

• 1 pair of parallel sides

• 2 pairs of parallel sides AND 4 equal sides

• 2 pairs of parallel lines

• 4 equal sides

Answer explanation

A rhombus is defined as a quadrilateral with 2 pairs of parallel sides and all 4 sides equal in length. Therefore, the correct choice is '2 pairs of parallel sides AND 4 equal sides'.

Which quadrilateral(s) have opposite sides that are congruent?

• Parallelogram

• Rectangle

• Square

• Rhombus

• Trapezoid

Answer explanation

A parallelogram, rectangle, square, and rhombus all have opposite sides that are congruent. In contrast, a trapezoid only has one pair of parallel sides, so it does not meet this criterion.

Which of these must have congruent diagonals? Check all that apply.

• Rectangle

• Square

• Rhombus

• Parallelogram

• Trapezoid

Answer explanation

Rectangles and squares have congruent diagonals due to their right angles and equal side lengths, respectively. In contrast, rhombuses and parallelograms do not guarantee congruent diagonals, and trapezoids do not either.

What is the sum of a quadrilateral's interior angles?

• 180

• 360

• 400

• 240

Answer explanation

The sum of a quadrilateral's interior angles is calculated using the formula (n-2) * 180, where n is the number of sides. For a quadrilateral (4 sides), it is (4-2) * 180 = 360 degrees. Thus, the correct answer is 360.

What are the attributes of a QUADRILATERAL?

• closed

• a plane figure

• 2D

• four sides

• at least 3 angles

Answer explanation

A quadrilateral is a closed, 2D plane figure with four sides and at least 3 angles. The attributes 'closed', 'a plane figure', '2D', and 'four sides' correctly describe its characteristics.

Match the following:

• trapezium

• 
• rhombus

• 
• kite

• 
• parallelogram

• 
• rectangle

•