Quadrilaterals on the Coordinate Plane Lesson 92 Quadrilaterals on the Coordinate Plane

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

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

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

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

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

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

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…?

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.

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.

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

Questions?