Coordinate Proof Packet- Day 3
Essential Question: How can I use
coordinate geometry to prove a
trapezoid?
Warm-Up:
Proving a Quadrilateral is a Trapezoid
•
•
Method: Show one pair of sides are parallel (same slope) and one pair of sides are not parallel
(different slopes).
Example 1: Prove that KATE a trapezoid with coordinates K(0,4), A(3,6), T(6,2)
and E(0,-2).
Show:
•
Formula: 𝒎 =
•
•
•
•
•
•
•
•
Work
Calculate the Slopes of all four sides to show 2 sides are parallel and 2 sides are nonparallel.
•
•
slope of _______:
•
Statement: ____ is a Trapezoid because____________________________
•
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
slope of _______:
=
slope of _______:
=
slope of _______:
=
=
∴__________||_______ and _______||_______
.
Proving a Quadrilateral is an Isosceles Trapezoid
•
•
Method: First, show one pair of sides are parallel (same slope) and one pair of sides are not parallel (different
slopes). Next, show that the legs of the trapezoid are congruent.
Example 2: Prove that quadrilateral MILK with the vertices M(1,3), I(-1,1), L(-1, -2), and K(4,3) is an isosceles
trapezoid.
Show:
•
Formula: 𝐦 =
•
Work
Step 1: Calculate the Slopes of all four sides to show 2 sides are parallel and 2 sides are nonparallel.
•
•
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
and 𝒅 =
(𝒙𝟐 − 𝒙𝟏 )𝟐 +(𝒚𝟐 − 𝒚𝟏 )𝟐
=
slope of _______:
•
•
slope of _______:
=
•
slope of _______:
=
•
slope of _______:
=
•
•
∴ _____________ and _____________________.
Step 2: Step 2: Calculate the distance of both non-parallel sides(legs) to show legs congruent.
•
________ = (
)𝟐 +(
)𝟐 = (
)2 + (
)2 =
+
=
•
________ = (
)𝟐 +(
)𝟐 = (
)2 + (
)2 =
+
=
•
•
∴ _______ ≅_________
Statement:
is an Isosceles Trapezoid because _______________________________________
___________________________________________________________________________________________.