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Coordinate Proof

Total questions: 20

Worksheet time: 54mins

Name
Class
Date
1.

To prove a quadrilateral is a rhombus you must also...

(Select all that apply)

a)

Prove it is a square

b)

Prove it is a parallelogram

c)

Prove that the diagonals are perpendicular

d)

Prove that the diagonals are congruent

2.

Prove the shape is a trapezoid.

a)

The slope of the parallel bases is 4/3

b)

The slope of the parallel bases is -4/3

c)

It is not a trapezoid because the slopes do not match.

d)

It is not a trapezoid because the legs are not parallel.

3.

Select the graph that represents an isosceles right triangle with leg length p in the most convenient way.

a)
b)
c)
d)
4.

Select the most convenient graph to represent a scalene triangle with one side length of 2m.

a)
b)
c)
d)
5.

Write a plan for the proof.

Given Coordinates of vertices of △OPM and △ONM

Prove △OPM and △ONM are isosceles triangles

a)

Find the lengths of OP, PM, MN, NO and OM to show that △OMP≅△OMN by the SSS Congruence Theorem.

b)

Find the lengths of OP, PM, MN, and NO to show that OP ≅ PM and MN ≅ NO.

6.

Write a plan for the proof. 

Given: G is the midpoint of HF
Prove: △GHJ≅△GFO

a)

Find the coordinates of G using the Midpoint Formula
Use these coordinates and the Distance formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ FGO by the Vertical Angles Congruence Theorem.

b)

Find the coordinates of G using the Distance Formula
Use these coordinates and the Midpoint formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.

c)

Then, use the SAS Congruence Theorem to conclude that △GHJ ≅ △GFO.

d)

Then, use the SSS Congruence Theorem to conclude that △GHJ ≅ △GFO.

7.

Find the coordinates of the vertex U.

a)

(k, 0)

b)

(0, k)

c)

(k, 2k)

d)

(2k, k)

8.

How would you prove a quadrilateral is a square using distance formula? (Check both)

a)

Prove there are 4 right angles

b)

Prove all 4 sides are congruent

c)

Prove diagonals are congrunt

d)

Prove opposite sides are parallel

9.

How would you prove that a triangle is isosceles?

a)

Find the distance of all 3 sides.

b)

Find the slopes of each side

c)

Find distance and determine that 2 of the 3 sides are the same.

d)

Cannot determine

10.

How would you prove a quadrilateral is a rhombus using distance formula?

a)

Prove diagonals are perpendicular

b)

Prove there are 4 congruent sides

c)

Prove opposite sides are parallel

d)

Prove there are 4 right angles

11.

How would you prove that a triangle is a right triangle? Check all that apply.

a)

Find the distance of each side and then use Pythagorean Theorem

b)

Find the midpoints

c)

Find the slopes of each side and determine if one pair has slopes that are negative reciprocals

d)

Find the vertices

12.

You have plotted the parallelogram in the picture. What is the slope of line BC without having to use the slope formula?

a)

0

b)

Undefined

13.

You have plotted the parallelogram in the picture. Which sides would you want to find the slope of first?

a)

AB and BC

b)

AB and AD

c)

AD and DC

d)

AB and DC

14.

Analyze the graph. Using distance formula, can you prove this is a rectangle?

a)

Yes, because AD = BC = 10 and AB = CD = 5

b)

No because  AD=210AD=2\sqrt{10}  and  BC=10BC=10   

c)

Yes because AD = BC = 5 and AB = CD = 10

d)

No because  CD=73CD=\sqrt{73}  and  BC=5BC=5  

15.

Analyze the graph. Using distance formula, can you prove this is a rhombus?

a)

Yes, all of the sides have a length of 3173\sqrt{17}

b)

No, because BC=317BC=3\sqrt{17} and AB=5AB=5

c)

Yes all of the sides have a length of 5

d)

No, because BC=5BC=5 and AB=317AB=3\sqrt{17}

16.

Brad proved that ABCD is a parallelogram by proving both sets of opposite sides to be parallel. What should he do next if he wants to prove it is a rhombus?  

a)

Find the distance of each line to see if they are congruent. 

b)

Compare the slopes of adjacent sides to see if they are perpendicular. 

17.

You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.

The distance from the campsite to you is ______ meters.

a)

1500

b)

1300

c)

1200

d)

1000

18.

Use the distance formula to see if side AB is congruent to side BC.

a)

Yes they are congruent

b)

No, they are not congruent

19.

Use the distance formula to see if side BC is congruent to side AD.

a)

Yes they are congruent

b)

No, they are not congruent

20.

Sarah proved that this is a square. The slopes of -2/5 and 5/2 made her able to do this. How come?

a)

Because those slopes form parallel lines.

b)

Because those slopes form perpendicular lines, creating right angles.

c)

Because those slopes make the sides congruent.