(a)
To describe the way to determine if the trapezoids in the design are isosceles.
(a)
Explanation of Solution
Given:
The following is the given design-
Calculation:
If the legs of a trapezoid are congruent, then it is an isosceles trapezoid.
The legs of each trapezoid are part of the diagonals of the larger square.
The diagonals of a square bisect the
If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid. (Isosceles Trapezoid Theorem)
Isosceles Trapezoid Theorem shows that the trapezoids in the design are isosceles.
(b)
To find theperimeter of one of the trapezoids.
(b)
Answer to Problem 43SGR
Explanation of Solution
Given:
The perimeter of the larger square is
Calculation:
The side length of the larger square is
Find the diagonal of the larger square
The side length of the smaller square is
Find the diagonal of the smaller square
Thus, the length of each leg of a trapezoid is
Find the perimeter of one trapezoid in the design.
Hence, the perimeter of one trapezoid is
Chapter 6 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Probability and Statistics for Engineers and Scientists
Elementary Statistics (13th Edition)
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Elementary Statistics: Picturing the World (7th Edition)
A First Course in Probability (10th Edition)
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning