**Classifying Quadrilaterals In The Coordinate Plane Worksheet Pdf** – Coordinate Proof for Parallel Opening Routine Determine whether the following quadrilateral is parallel for the given values of the variables. x=6y=3.5

Coordinate Proof for a Parallelogram Objective: Use coordinate geometry to prove that a quadrilateral is a parallelogram. Key Question: What criteria can be used in coordinate proof to determine whether a quadrilateral is a parallelogram?

## Classifying Quadrilaterals In The Coordinate Plane Worksheet Pdf

Coordinate Proof for Vocabulary Parallelogram Parallelogram: It is a quadrilateral with two pairs of parallel sides. Rectangle: It is a square with four right angles. Rhombus: This is a simple square with all four sides of the same length. Square: A square is a regular square, meaning it has four equal sides and four equal angles.

### Ordered Pairs On The Coordinate Plane Activity

Coordinate Vocabulary Proof Trapezoid parallelogram: It is a quadrilateral in which two opposite sides are parallel. The parallel sides are called “bases”. Isosceles Trapezoid: This is a special type of trapezoid where the non-parallel sides and base angles are equal. Kite: It is a quadrilateral whose four sides can be grouped into two pairs of equal sides adjacent to each other.

Coordinate proof for parallelism Four different criteria can be used to prove whether a quadrilateral is a parallelogram in the coordinate plane: distance formula, to determine whether the two opposite sides are equal. Slope type to determine if two opposite sides are parallel. Midpoint formula to determine if diagonals intersect. Distance formula and slope formula to determine if a pair of opposite sides are parallel and equal.

Proof of coordinates for a parallel guided exercise – WE DO The vertices of the JOHN quadrilateral are J (3, 1), O (3, 3), H (5, 7) and N (1, 5). Use coordinate geometry to prove that square JOHN is a parallelogram.

Coordinate Proof for Parallelism Guided Practice – WE DO use the distance formula and the slope formula to determine if the quadrilateral is a parallelogram.

### Classifying Quadrilaterals On The Coordinate Plane (video)

Proof of coordinates for a parallel guided exercise – we determine if the figure with the given vertices is parallel, P (5, 3), Q (1, 5), R (6, 1), S (2 , 7)

Proof of coordinates for a parallel guided exercise – we determine if the figure with the given vertices is parallel, P (5, 3), Q (1, 5), R (6, 1), S (2 , 7) then PQRS is parallelogram

Proof of coordinates for parallel independent practice – YOU DO worksheet Proof of coordinates for parallel exercises 1 to 4

Coordinate Proof for Closing Parallelism Key Question: What criteria can be used in coordinate proof to determine whether a quadrilateral is a parallelogram?

## Geometry_chapter_8 Pages 51 100

In order for this site to work, we collect user data and transfer it to processors. To use this site, you must agree to our privacy policy, including our cookie policy.1 Name: Class: Date: ID: Geometry Unit 4 Multiple Choice Practice Exam Unit 2 Identify the options that best complete the statement or they answered the question. 1. Which diagram shows the most accurate position and marking of an isosceles trapezoid in the coordinate plane? one. to do. si. That is 1

2 Name: ID: A 2. Which diagram shows the most logical position of a rectangle in the first quadrant of a coordinate plane? one. to do. si. ie short answer 3. Is the TVS uneven, isosceles or equilateral? The vertices are T(1, 1), V(4, 0) and S(2, 4). 4. A quadrilateral has vertices ( 3, 1), (4, 5), ( 1, 5) and ( 3, 3). What special quadrilateral is formed by connecting the midpoints of the sides? 5. In the coordinate plane, the three vertices of rectangle ABCD are A(0, 0), B(0, a) and D(b, 0). What are the coordinates of point C? 6. The vertices of the trapezoid together with A(4p, 4q), B(4r, 4q) and C(4s, 0) are the origin. Find the midpoint of the middle part of the trapezoid. 2

3 Name: ID: A 7. For the parallelogram, find the coordinates of P without using new variables. 8. For A(1, 1), B(2, 1) and C(2, 1), find all the locations of a quarter point D such that a parallelogram is formed using A, B, C, D as a vertex order. Enter each point D into a coordinate grid and draw the parallel. 9. The fact that the diagonals of a kite are vertical indicates a way of placing a kite in the coordinate plane. See this location. Add captions to kite shirts. 10. Show how to place a rhombus in the coordinate plane so that its diagonals are along the axes. Label the vertices using as few variables as possible. 11. Find the lengths of the diagonals of this trapezoid. 12. On the coordinate plane draw a square with sides of 8n units. Give the coordinates of each vertex and the coordinates of the intersection of the diagonals. 3

4 Name: ID: Essay 13. Prove that the parallelogram ABCD with vertices A( 5, 1), B( 9, 6), C( 1, 5) and D(3, 2) is a rhombus by showing that it is A rhombus is a parallelogram with vertical diagonals. 14. Find the center of each side of the kite. Connect the midpoints. What is the most accurate classification of the quadrilateral formed by joining the midpoints of the sides of the kite? 15. Prove in coordinate geometry: the centers of the sides of a rhombus define a rectangle. 16. Prove using coordinate geometry: if a point lies on the halfway point of a line segment, then it is equidistant from the endpoints of the line segment. 17. Write a coordinate proof for the following theorem: If a parallelogram is a rectangle, then its diagonals are equal. 4

### Th Grade Geometry

5 Name: ID: A Other 18. Draw in the coordinate plane JKL with J(2, 3), K(10, 4) and L(8, 9). JKL classification. explain. 19. On the coordinate plane draw the parallelogram ABCD with A( 5, 0), B(1, 7), C(8, 1) and D(2, 6). Then show that ABCD is a rectangle. 20. AC is a segment in the coordinate plane. Explain why it is sometimes useful to give points A and C the coordinates (2a, 2b) and (2c, 2d). 21. If you wanted to use coordinate geometry to prove that the diagonals of a parallelogram intersect, how would you place the parallelogram in the coordinate plane? Specify the coordinates of the vertices for the location you selected. 22. Write the given theorems and prove to prove the following theorem: If a quadrilateral is a square, then its diagonals are perpendicular to each other. Square FGHK and its diagonals are for you. 23. Write a coordinate proof for the following theorem: If a square is a kite, then its diagonals are perpendicular to each other. 5

6 Geometry Unit 4 Unit 2 Practice Part Practice Answer Multiple Choice 1. ANS: A PTS: 1 DIF: L3 REF: 6-8 Applying Coordinate Geometry Top: 6-8 Task 1 Naming Coordinates KEY: Algebra plane coordinate isosceles. ANS: A PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Task 1 Naming Coordinates KEY: Algebra Coordinates Plane Rectangle Square DOC: DOC 1 Short Answer 3. ANS: Isosceles PTS: 1 DIF : L2 REF: 6-7 Polygons in the coordinate plane OBJ: Sort polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA. 912.G.4.1 MA.912.G.4.8 TOP: 6-7 TASK 1 TRIANGLE CLASSIFICATION ASSUMPTION: Non-uniform isosceles triangle distance type 4. ANS: kite PTS: 1 DIF: L3 REF: 6-7 polygons in the coordinate plane OBJ : polygons sorted in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912 .G 4.8 TOP: 6-7 Task 3 Square Classification 5. ANS: (b,a) LEG: Parallelogram Center PTS: 1 DIF: L 2 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Task 2 Using Variable Coordinate Legend: Rectangle Coordinates Algebra level 1

7 ANS 6: (p + r + s, 2q) PTS: 1 DIF: L3 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Problem 2 Using Coordinate Variables KEY: Coordinate Algebra Coordinate Plane Isosceles Mid-Trapezoid ANS 7 : (a +c,b) PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Task 2 Using Coordinate Variables Legend: Rectangular Coordinate Plane Algebra 2

8 8. ANS: PTS: 1 DIF: L4 REF: 6-7 Polygons in the Coordinate Plane OBJ: Classify polygons in the coordinate plane STA: MA.912.G.1.1 MA.912.G.2.6 MA.912.G .3.1 MA. 912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 Topic: 6-7 Exercise 3 Quadrilateral Classification Assignment: Drawing a parallelogram of the coordinate plane facing multiple segments DOK question: DOK 3 3

## Lesson: The Coordinate Plane: First Quadrant

9 9. A: Answers may vary. EXAMPLE: PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Problem 1 Naming Coordinates KEY: Coordinate Plane Algebra Kite 10. Answers: Answers may vary. EXAMPLE: PTS: 1 DIF: L3 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Task 1 Naming Coordinates KEY: Coordinate Plane Algebra Rhombus 11. ANS: Each diagonal has length (a b) 2 c 2. PTS: 1 DIF: L4 REF: 6-8 Using Coordinate Geometry TOP: 6-8 Exercise 2 Using Coordinate Variables Legend: Algebra Coordinate Plane Isosceles Trapezoid Trapezoid Diagonal 4

10 12. ANS: PTS: 1 DIF: L3 REF: 6-8 Applying Coordinate Geometry TOP: 6-8 Problem 2 Using Variable Coordinates KEY: Square Algebraic Coordinate Review 13. ANS: [4] Show that ABCD is parallelogram ( in one from several methods). Then prove that the diagonals are perpendicular by calculating the slopes

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