Problem Analysis:
The task involves
decomposing 2D shapes into smaller, simpler shapes. The goal is to identify which of the given options correctly represents the decomposition of a larger shape into its constituent parts.
Step-by-Step Solution:
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Part 1: Decomposing the Pentagon (Shape on the Left)
1.
Shape to Decompose: The left shape is a
pentagon.
2.
Options Provided:
-
Option A: Two triangles.
-
Option B: Three triangles.
-
Option C: Four triangles.
-
Option D: Five triangles.
3.
Analysis:
- A pentagon can be divided into triangles by drawing diagonals from one vertex to all non-adjacent vertices.
- If we draw two diagonals from one vertex of the pentagon, it will divide the pentagon into
three triangles.
- Therefore, the correct decomposition is
three triangles.
4.
Correct Answer:
Option B.
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####
Part 2: Decomposing the Circle and Triangle (Shape on the Right)
1.
Shape to Decompose: The right shape consists of a
circle and a
triangle.
2.
Options Provided:
-
Option A: One circle and one triangle.
-
Option B: Two circles and one triangle.
-
Option C: One circle and two triangles.
-
Option D: Two circles and two triangles.
3.
Analysis:
- The given shape already consists of a single circle and a single triangle.
- There are no additional shapes or subdivisions that suggest more than one circle or more than one triangle.
- Therefore, the correct decomposition is
one circle and one triangle.
4.
Correct Answer:
Option A.
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####
Part 3: Decomposing the Rectangle with a Cut (Shape Below Left)
1.
Shape to Decompose: The bottom-left shape is a
rectangle with a horizontal cut through its middle.
2.
Options Provided:
-
Option A: Two rectangles.
-
Option B: Three rectangles.
-
Option C: Four rectangles.
-
Option D: Five rectangles.
3.
Analysis:
- The rectangle is divided into two equal horizontal sections by the cut.
- Each section is itself a rectangle.
- Therefore, the decomposition results in
two rectangles.
4.
Correct Answer:
Option A.
---
####
Part 4: Decomposing the Arrow (Shape Below Right)
1.
Shape to Decompose: The bottom-right shape is an
arrow.
2.
Options Provided:
-
Option A: One rectangle and two triangles.
-
Option B: Two rectangles and one triangle.
-
Option C: Three rectangles.
-
Option D: Two rectangles and two triangles.
3.
Analysis:
- The arrow can be broken down into:
- A
rectangle forming the body of the arrow.
- Two
triangles forming the head of the arrow.
- Therefore, the decomposition results in
one rectangle and two triangles.
4.
Correct Answer:
Option A.
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Final Answers:
1. For the pentagon:
Option B
2. For the circle and triangle:
Option A
3. For the rectangle with a cut:
Option A
4. For the arrow:
Option A
Boxed Final Answer:
\[
\boxed{B, A, A, A}
\]
Parent Tip: Review the logic above to help your child master the concept of composing and decomposing shapes worksheet.
