a.
To classify : The statement as true and false.
a.
Answer to Problem 6MRE
The statement is true.
Explanation of Solution
Given information :
All square are similar.
Calculation :
Since, the sides are always proportional.
Therefore, all square are similar.
Hence,
The statement is true.
b.
To classify : The statement as true and false.
b.
Answer to Problem 6MRE
The statement is false.
Explanation of Solution
Given information :
All rectangles are similar.
Calculation :
Since, there are rectangles whose corresponding sides may not be proportional.
Therefore, all rectangles are not similar.
Hence,
The statement is false.
c.
To classify : The statement as true and false.
c.
Answer to Problem 6MRE
The statement is true.
Explanation of Solution
Given information :
All
Calculation :
Since, all circles have proportional radii.
Therefore, all circles are similar.
Hence,
The statement is true.
d.
To classify : The statement as true and false.
d.
Answer to Problem 6MRE
The statement is false.
Explanation of Solution
Given information :
All rhombuses are similar.
Calculation :
Since, all rhombuses have proportional sides but their corresponding
Therefore, all rhombuses are not similar.
Hence,
The statement is false.
e.
To classify : The statement as true and false.
e.
Answer to Problem 6MRE
The statement is false.
Explanation of Solution
Given information :
All right
Calculation :
Since, the sides of all right triangle are not proportional.
Therefore, all rhombuses are not similar.
Hence,
The statement is false.
f.
To classify : The statement as true and false.
f.
Answer to Problem 6MRE
The statement is true.
Explanation of Solution
Given information :
All equilateral triangles are similar.
Calculation :
Since, the sides of all equilateral triangles are proportional and their angles are always 60°.
Therefore, all equilateral triangles are similar.
Hence,
The statement is true.
g.
To classify : The statement as true and false.
g.
Answer to Problem 6MRE
The statement is true.
Explanation of Solution
Given information :
All regular pentagons are similar.
Calculation :
Since, the sides of all regular pentagons are proportional and their angles are always congruent.
Therefore, all regular pentagons are similar.
Hence,
The statement is true.
h.
To classify : The statement as true and false.
h.
Answer to Problem 6MRE
The statement is false.
Explanation of Solution
Given information :
All isosceles trapezoids are similar.
Calculation :
Since, the sides of all isosceles trapezoids are not proportional and their corresponding angles are not congruent.
Therefore, all isosceles trapezoids are not similar.
Hence,
The statement is false.
Chapter 12 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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- 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