O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°. O B. No, because a vertex figure cannot be formed with different types of polygons. O C. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons. O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.2: Similar Polygons
Problem 11E: a Does the similarity relationship have a reflexive property for triangles and polygons in general?...
icon
Related questions
Question
O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°.
O B. No, because a vertex figure cannot be formed with different types of polygons.
OC. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons.
O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.
Transcribed Image Text:O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°. O B. No, because a vertex figure cannot be formed with different types of polygons. OC. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons. O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.
Wailea noticed that, since two adjacent equilateral triangles, a square, and a dodecagon form a vertex figure
such as that shown at A, there should be a semiregular tiling in which this vertex figure occurs at every vertex.
(a) Is Wailea correct that these four polygons create a vertex figure at A?
(b) Explain to Wailea why the vertex figure does not extend to a semiregular tiling.
B
Transcribed Image Text:Wailea noticed that, since two adjacent equilateral triangles, a square, and a dodecagon form a vertex figure such as that shown at A, there should be a semiregular tiling in which this vertex figure occurs at every vertex. (a) Is Wailea correct that these four polygons create a vertex figure at A? (b) Explain to Wailea why the vertex figure does not extend to a semiregular tiling. B
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning