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Name Date Class LESSON 9-2 Conditions for Parallelograms Practice and Problem Solving A/B Determine whether the figure is a parallelogram for the given values of the variables. Explain your answers. 1. x 9 and y 11 2. a 4. 3 and b 13 A quadrilateral has vertices E 1 1 F 4 5 G 6 6 and H 3 2. Complete Problems 3 6 to tell whether EFGH is a parallelogram* 3. Plot the vertices and draw EFGH. 4. Use the Pythagorean theorem to find the lengths of sides EF and HG* EF HG 5. Use the Slope Formula to find the slopes of sides EF and GH. slope of EF slope of HG 6. The answers to Problems 4 and 5 reveal something about figure EFGH. State the theorem that uses these facts to prove that EFGH is a parallelogram* Use the given method to determine whether the quadrilateral with the given vertices is a parallelogram* 7. Find the slopes of all four sides J 4 1 K 7 4 L 2 10 M 5 7. 8. Find the lengths of all four sides P 2 2 Q 1 3 R 4 2 S 3 7. Original content Copyright by Houghton Mifflin Harcourt. Additio....

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  1. Press the ‘Get Form’ button to access the form and display it in the editor.
  2. Begin by entering your name, date, and class in the designated fields at the top of the form. This information will help identify who has completed the document.
  3. For questions regarding specific values, enter the given values for variables x, y, a, and b in the appropriate sections. Ensure that you explain your reasoning for each answer carefully.
  4. Move on to the section that involves plotting the vertices of the quadrilateral EFGH. Use the provided coordinates to accurately draw the figure on your digital platform.
  5. Utilize the Pythagorean theorem to calculate the lengths of sides EF and HG. Enter the calculated values in the respective blanks.
  6. Calculate the slopes of sides EF and HG using the Slope Formula, and fill in the corresponding blanks with your results.
  7. Discuss the conclusions drawn from the lengths and slopes calculated in the previous steps. State the theorem that supports your findings about EFGH being a parallelogram.
  8. Proceed to find the slopes and lengths for the quadrilateral with vertices J, K, L, and M. Input your calculations in the relevant sections.
  9. Once you have filled in all sections, review your answers for accuracy. Save your changes, and you may choose to download, print, or share the form as needed.

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Parallelogram: A parallelogram is a four-sided, two-dimensional shape that satisfies the following conditions: Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent.

There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). Opposite angels are congruent (D = B). Consecutive angles are supplementary (A + D = 180°). If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other.

Conditions for Parallelograms Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. The diagonals bisect each other. One angle is supplementary to both its consecutive angles.

If a quadrilaterals is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary ($$ x + y =180). If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Opposite sides of a parallelogram are congruent. Opposite angles are congruent. Consecutive angles are supplementary. The diagonals bisect each other.

Match Opposite Sides are parallel. Opposite Sides are congruent. Opposite Angles are congruent. Consecutive Angles are supplementary. Diagonals bisect each other.

1:15 16:14 6-2 Properties of Parallelograms - YouTube YouTube Start of suggested clip End of suggested clip Alright so let's take a look at why this is. Okay I know that these sides are parallel so we'reMoreAlright so let's take a look at why this is. Okay I know that these sides are parallel so we're looking at this angle here and this angle. Here notice they are same side interior angles.

In a parallelogram, all angles are congruent. In a parallelogram, consecutive angles are congruent. In a parallelogram, consecutive angles are supplementary. In a parallelogram, consecutive sides are perpendicular.

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