1. Quadrilaterals on the Coordinate Plane
Lesson 92
Quadrilaterals on the Coordinate Plane

2. Parallelogram Review Opposite sides parallel Opposite sides congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
One pair of opposite sides both parallel and congruent

3. Rectangle Review Quadrilateral with 4 rt. ∠’s
Parallelogram with 1 rt. ∠
Parallelogram with ≅ diagonals

4. Rhombus Review Quadrilateral with 4 ≅ sides
Parallelogram with ⊥ diagonals
Parallelogram with diagonals bisecting opposite angles

5. Square Review Show the parallelogram is a rhombus and a rectangle
⊥ & ≅ diagonals
4 ≅ sides & 1 rt. ∠
≅ diagonals & 4 ≅ sides …

6. Trapezoid Review Bases are parallel 𝐵𝐶 & 𝐴𝐷 Legs are nonparallel sides
𝐵𝐶 & 𝐴𝐷
Legs are nonparallel sides
𝐴𝐵 & 𝐷𝐶
Isosceles Trapezoid:
Base angles are congruent
∠A ≅ ∠ D & ∠ B ≅ ∠ C
Legs are congruent
𝐴𝐵 ≅ 𝐷𝐶
Diagonals are congruent
𝐴𝐶 ≅ 𝐵𝐷

7. Properties of a Kite ∠B & ∠ D are bisected ∠ ABE≅ ∠ CBE ∠ ADE≅ ∠ CDE
Diagonals of a kite are perpendicular
A= ½(d1 x d2 )
𝐴𝐸 ≅ 𝐸𝐶
∠A≅ ∠C
∠B & ∠ D are bisected
∠ ABE≅ ∠ CBE
∠ ADE≅ ∠ CDE

8. What can be shown on a coordinate plane?
How can you show sides are parallel?
How can you show diagonals are perpendicular/rt. ∠?
How can you show sides are congruent?
How can you show diagonals are congruent?
Can you show congruent angles in a coordinate plane?
Use slope formula to show slopes are equal
Use slope formula to show their product is -1
Use distance formula to show segments have = measures
With the except of rt. or straight ∠’s, NO…?

9. Is EFGH a parallelogram when E(1, 6), F(5, 7), G(7, 2) & H(3, 1)
𝑚 𝐸𝐹 = 7−6 5−1 = 1 4 𝑚 𝐹𝐺 = 2−7 7−5 = −5 2 𝑚 𝐺𝐻 = 2−1 7−3 = 1 4 𝑚 𝐻𝐸 = 1−6 3−1 = −5 2 Yes, opposite sides are parallel.

10. Is JKLM a trapezoid when J(0, 4), K(4, 6), L(4, 2) & M(2, 1)
𝑚 𝐽𝐾 = 6−4 4−0 = 1 2
𝑚 𝐾𝐿 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
𝑚 𝐿𝑀 = 2−1 4−2 = 1 2
𝑚 𝑀𝐽 = 1−4 2−0 = −3 2
Yes, one pair is parallel & the other pair is not.

11. What type of quadrilateral is PQRS when P(4, 6), Q(7, 4), R(4, 2) & S(1, 4)
𝑃𝑄= 7− −6 2 = 13 𝑄𝑅= 4− −4 2 = 13 𝑅𝑆= 1− −2 2 = 13 𝑆𝑃= 4− −4 2 = 13 Rhombus, but could be a square. 𝑃𝑅=4 𝑆𝑄=6 Not a square. PQRS is a rhombus

12. Questions?