Use the properties of quadrilaterals to determine the number of quadrilaterals that can be constructed with congruent opposite sides and supplementary consecutive angles.
Given the properties of quadrilaterals, we know that opposite sides of a quadrilateral are congruent in a parallelogram. Additionally, we know that consecutive angles in a quadrilateral add up to 360 degrees.
Since the quadrilateral has congruent opposite sides, it must be a parallelogram. In a parallelogram, consecutive angles are supplementary, meaning they add up to 180 degrees.
Therefore, the only quadrilateral that can be constructed with congruent opposite sides and supplementary consecutive angles is a parallelogram. So, there is only one quadrilateral that fits these criteria.
Identify the quadrilaterals that can be constructed with congruent diagonals that bisect each other.
Quadrilaterals that can be constructed with congruent diagonals that bisect each other are called parallelograms. In a parallelogram, the diagonals bisect each other and are congruent. So, any quadrilateral with these properties must be a parallelogram.
Therefore, the only quadrilateral that can be constructed with congruent diagonals that bisect each other is a parallelogram.
What types of quadrilaterals can you construct with at least one pair of opposite parallel sides but consecutive angles that are not supplementary?
If a quadrilateral has at least one pair of opposite parallel sides, it is a trapezoid. In a trapezoid, one pair of opposite sides are parallel, but the consecutive angles are not necessarily supplementary.
Therefore, the types of quadrilaterals that can be constructed with at least one pair of opposite parallel sides but consecutive angles that are not supplementary are trapezoids.
ready for one that is hard for you to comprehend?
I'll do my best to assist you! Please go ahead and present the challenge to me.
Courtney is constructing quadrilateral EFGH , where EF=6 cm , FG=2 cm , EH=5 cm , ∠HEF=60° , and ∠EFG=140° . Courtney starts by drawing line segment EF=6 cm , as shown here. If she wants to locate point H next, what should Courtney do?
To locate point H in quadrilateral EFGH after drawing line segment EF=6 cm, Courtney should follow these steps:
1. Draw a line segment FG with a length of 2 cm starting from point F.
2. Use a protractor to draw angle EFG=140° at point F. This will determine the direction of line segment FG.
3. From point G, draw a line segment GH with a length of 5 cm to complete the quadrilateral EFGH.
I hope this helps Courtney in locating point H in constructing quadrilateral EFGH!
Keep that question in mind.
Now what is the answer to the question, these are the responses.
A. Starting at point E, use a protractor to draw a ray that makes a 60° angle with line segment EF.
B. Starting at point F, use a protractor to draw a ray that makes a 140° angle with line segment EF.
C. Starting at point F, use a protractor to draw a ray that makes a 60° angle with line segment EF.
D. Starting at point E, use a ruler to draw line segment EH=5 cm.