Coordinate Proof

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.

Tags

CCSS.6.G.A.3

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

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Tags

CCSS.HSG.CO.A.2

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

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Tags

CCSS.6.G.A.3

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.

Tags

CCSS.HSG.SRT.B.5

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)

Tags

CCSS.HSG.GPE.B.6

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

Tags

CCSS.HSG.C.A.3

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

Tags

CCSS.HSG.CO.B.7