Day 11 Rhombus Proof Hebbard Manning.notebook
November 04, 2013
DO NOW Draw in your Notebooks:
If a quadrilateral has 2 pairs of parallel sides then it is a parallelogram (Slope) If a quadrilateral has 2 pairs If a quadrilateral has of parallel sides AND a right angle
all four equal sides then it is a rectangle (Slope) then it is a rhombus.
(distance)
A rhombus is a special type of parallelogram in which all 4 sides are congruent
I know what you are thinking...
so what is the difference between a rhombus and a square?
• a square also has four ninety degree angles where a rhombus does not
Day 11 Rhombus Proof Hebbard Manning.notebook
November 04, 2013
Rhombus Proofs
Objective: Students will apply their knowledge of rhombus properties to prove that a quadrilateral is a rhombus.
GG 69
1. Given quadrilateral ABCD whose vertices are A(­3, 2), B(­2, 6), C(2, 7) and D(1, 3) prove that it is a rhombus.
y
1)
C
B
1) Graph
2) If a quadrilateral has all four sides are equal then it is a rhombus.
3) d = (x1­x2)2 + (y1=y2)2
A
D
x
4) d AB = (­3­­2)2+(2­6)2 d BC = (­2­2)2+(6­7)2 = 16+1 = 17 = 1+16 = 17 d CD = (2­1)2+(7­3)2 d AD = (­3­1)2+(2­3)2 = 1+16 = 17
= 16+1 = 17 5) d AB = d BC = d CD = d AD
6) Quadrilateral ABCD is a Rhombus
Day 11 Rhombus Proof Hebbard Manning.notebook
November 04, 2013
2. Given quadrilateral ABCD whose vertices are A(­2, ­1), B(4, ­2), C(3, ­8) and D(­3,­7) prove that it is a rhombus.
y
1) Graph
2) If a quadrilateral has all four sides are equal then it is a rhombus.
3) d = (x1­x2)2 + (y1=y2)2
4) d AB = (­2­4)2+(­1­­2)2 d BC = (4­3)2+(­2­­8)2 A
B
x
= 36+1 = 37
= 1+36 = 37
d CD = (3­­3)2+(­8­­7)2 d AD = (­2­­3)2+(­1­­7)2 = 36+1 = 37
= 1+36 = 37
5) d AB = d BC = d CD = d AD
D
C
6) Quadrilateral ABCD is a Rhombus
Exit Ticket: Explain what makes a rhombus different from a parallelogram.