Question

Conjecture about the properties that change and the properties that stay the same when creating quadrilaterals that are not parallelograms. Check all that apply. The sum of the interior angles will still be 360°. Both pairs of opposite sides will not be parallel. Both pairs of opposite sides will not be congruent. The diagonals will not bisect each other.

Answer 1

A quadrilateral is a four sided shape with two diagonals that bisects each other. The sum total of the interior angles is always 360° for any quadrilateral no matter the shape of the quadrilateral.

It must be noted that both pairs of opposite sides of some quadrilaterals are equal e.g Parallelogram while some are not e.g Trapezium, rhombus, trapezoid etc.

When creating quadrilaterals that are not parallelograms, the following property of such quadrilateral will therefore remains the same.

• The sum of the interior angles will still be 360°.

The following properties will change when creating quadrilaterals that are not parallelograms.

• Both pairs of opposite sides will not be parallel. e.g Trapezoids and rhombus

• Both pairs of opposite sides will not be congruent (will not be the same)

Answer 2

Options A and C are correct.

- The sum of the interior angles will still be 360°.

- Both pairs of opposite sides will not be congruent.

Explanation:

Complete Question

alyssamonae02

04/20/2020

Mathematics

Middle School

+5 pts

Answered

Conjecture about the properties that change and the properties that stay the same when creating quadrilaterals that are not parallelograms. The new quadilateral has angles

Angle LMN = 85°

Angle MNO = 99°

Angle NOL = 81°

Angle OLM = 95°

Check all that apply.

- The sum of the interior angles will still be 360°.

- Both pairs of opposite sides will not be parallel.

- Both pairs of opposite sides will not be congruent.

- The diagonals will not bisect each other.

Solution

A sketch of the new quadilateral is provided in the attached image.

Checking the statements one at a time.

- The sum of the interior angles will still be 360°.

The sum of interior angles for all four sided plane figures is 360°, hence, the new quadilateral too, although, not a parallelogram anymore, will still have interior angles that sum up to 360°. So, this is a statement that doesn't change with change in figure from parallelogram to other quadilaterals.

- Both pairs of opposite sides will not be parallel.

We cannot tell if this is true just from the information on the angles provided.

- Both pairs of opposite sides will not be congruent.

This is evident as one of the condition for opposite sides to be congruent is for opposite angles too to be equal. None of the opposite angles are equal, hence, this statement is true too.

- The diagonals will not bisect each other.

This also isn't evident from the limited information provided. So, we cannot select it as a correct statement.

Hope this Helps!!!