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WorksheetsCoordinate Proof
Total questions: 20
Worksheet time: 54mins
To prove a quadrilateral is a rhombus you must also...
(Select all that apply)
Prove it is a square
Prove it is a parallelogram
Prove that the diagonals are perpendicular
Prove that the diagonals are congruent
Prove the shape is a trapezoid.
The slope of the parallel bases is 4/3
The slope of the parallel bases is -4/3
It is not a trapezoid because the slopes do not match.
It is not a trapezoid because the legs are not parallel.
Select the graph that represents an isosceles right triangle with leg length p in the most convenient way.
Select the most convenient graph to represent a scalene triangle with one side length of 2m.
Write a plan for the proof.
Given Coordinates of vertices of △OPM and △ONM
Prove △OPM and △ONM are isosceles triangles
Find the lengths of OP, PM, MN, NO and OM to show that △OMP≅△OMN by the SSS Congruence Theorem.
Find the lengths of OP, PM, MN, and NO to show that OP ≅ PM and MN ≅ NO.
Write a plan for the proof.
Given: G is the midpoint of HF
Prove: △GHJ≅△GFO
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.
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.
Then, use the SAS Congruence Theorem to conclude that △GHJ ≅ △GFO.
Then, use the SSS Congruence Theorem to conclude that △GHJ ≅ △GFO.
Find the coordinates of the vertex U.
(k, 0)
(0, k)
(k, 2k)
(2k, k)
How would you prove a quadrilateral is a square using distance formula? (Check both)
Prove there are 4 right angles
Prove all 4 sides are congruent
Prove diagonals are congrunt
Prove opposite sides are parallel
How would you prove that a triangle is isosceles?
Find the distance of all 3 sides.
Find the slopes of each side
Find distance and determine that 2 of the 3 sides are the same.
Cannot determine
How would you prove a quadrilateral is a rhombus using distance formula?
Prove diagonals are perpendicular
Prove there are 4 congruent sides
Prove opposite sides are parallel
Prove there are 4 right angles
How would you prove that a triangle is a right triangle? Check all that apply.
Find the distance of each side and then use Pythagorean Theorem
Find the midpoints
Find the slopes of each side and determine if one pair has slopes that are negative reciprocals
Find the vertices
You have plotted the parallelogram in the picture. What is the slope of line BC without having to use the slope formula?
0
Undefined
You have plotted the parallelogram in the picture. Which sides would you want to find the slope of first?
AB and BC
AB and AD
AD and DC
AB and DC
Analyze the graph. Using distance formula, can you prove this is a rectangle?
Yes, because AD = BC = 10 and AB = CD = 5
No because AD=210 and BC=10
Yes because AD = BC = 5 and AB = CD = 10
No because CD=73 and BC=5
Analyze the graph. Using distance formula, can you prove this is a rhombus?
Yes, all of the sides have a length of 317
No, because BC=317 and AB=5
Yes all of the sides have a length of 5
No, because BC=5 and AB=317
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?
Find the distance of each line to see if they are congruent.
Compare the slopes of adjacent sides to see if they are perpendicular.
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.
1500
1300
1200
1000
Use the distance formula to see if side AB is congruent to side BC.
Yes they are congruent
No, they are not congruent
Use the distance formula to see if side BC is congruent to side AD.
Yes they are congruent
No, they are not congruent
Sarah proved that this is a square. The slopes of -2/5 and 5/2 made her able to do this. How come?
Because those slopes form parallel lines.
Because those slopes form perpendicular lines, creating right angles.
Because those slopes make the sides congruent.
