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)
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
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2765c9e-58e5-40bf-b894-830babb98674%2F848f9974-134c-4cf8-9eb1-9563e2758881%2Fahgvini_processed.jpeg&w=3840&q=75)
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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