Sketch/create the following geometric shapes on distinct cartesian planes. Then, show important properties of the shapes by solving for the length of its sides and/or the slope of the sides.  1. Rectangle (Opposite sides are congruent and parallel; Adjacent sides are perpendicular)  2. Isosceles Trapezoid (1 pair of opposite sides are parallel; 1 pair of congruent non-parallel sides)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 45E
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Sketch/create the following geometric shapes on distinct cartesian planes. Then, show important properties of the shapes by solving for the length of its sides and/or the slope of the sides. 

1. Rectangle (Opposite sides are congruent and parallel; Adjacent sides are perpendicular) 

2. Isosceles Trapezoid (1 pair of opposite sides are parallel; 1 pair of congruent non-parallel sides)

3. Rhombus (4 congruent sides; adjacent sides does not have to be perpendicular; opposite sides are parallel)

D (3,5)
C (6,4)
A
B,
(1,-1)
(4,-2)
a. Opposite sides are congruent:
c. Adjacent Sides are Perpendicular
1
AB = V(4 – 1)2 +(-2+1)² = /10
MAB
3
DC = (6 – 3)² + (4 – 5)² = V10
%3D
mBc
= 3
AD = BC
AB 1 BC
AD = /(3 – 1)2 + (5 + 1)² = V40 = 2/10
MAD = 3
BC = (6 – 4)² + (4 + 2)² = V40 = 2/10
1
%3D
mpc
3
AD = BC
AD I DC
b. Opposite sides are parallel
-2 +1 1
MAB
4- 1
5 - 4
1
mpc =
3 -6
3
AB || DC
5 +1
= 3
3 - 1
MAD
4 + 2
= 3
- 4
%3D
AD || BC
Transcribed Image Text:D (3,5) C (6,4) A B, (1,-1) (4,-2) a. Opposite sides are congruent: c. Adjacent Sides are Perpendicular 1 AB = V(4 – 1)2 +(-2+1)² = /10 MAB 3 DC = (6 – 3)² + (4 – 5)² = V10 %3D mBc = 3 AD = BC AB 1 BC AD = /(3 – 1)2 + (5 + 1)² = V40 = 2/10 MAD = 3 BC = (6 – 4)² + (4 + 2)² = V40 = 2/10 1 %3D mpc 3 AD = BC AD I DC b. Opposite sides are parallel -2 +1 1 MAB 4- 1 5 - 4 1 mpc = 3 -6 3 AB || DC 5 +1 = 3 3 - 1 MAD 4 + 2 = 3 - 4 %3D AD || BC
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