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.
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?...
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddb6d050-560d-48f0-9a76-40cbd2b28dda%2F133d3ba2-6897-4e50-b2c4-098113ce2135%2F0s59q36_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddb6d050-560d-48f0-9a76-40cbd2b28dda%2F133d3ba2-6897-4e50-b2c4-098113ce2135%2Fe51rr6v9_processed.png&w=3840&q=75)
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
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