Problem Analysis:
The task is to count the number of triangles in two given geometric shapes. Let's solve this step by step for each shape.
---
Shape 1:
The first shape is a large triangle divided into smaller triangles by internal lines. Here’s how we can count the triangles:
#### Step 1: Identify individual triangles.
- There are
4 small triangles at the corners of the large triangle.
#### Step 2: Identify composite triangles.
- The four small triangles combine to form
1 larger triangle (the entire shape).
#### Step 3: Count all triangles.
- Total triangles = 4 (small) + 1 (large) =
5 triangles.
Thus, the total number of triangles in the first shape is
5.
---
Shape 2:
The second shape is also a large triangle divided into smaller triangles by internal lines. Let’s count the triangles systematically:
#### Step 1: Identify individual triangles.
- There are
7 small triangles visible in the shape.
#### Step 2: Identify composite triangles.
-
Medium-sized triangles: There are
3 medium-sized triangles formed by combining some of the small triangles.
-
Large triangle: The entire shape itself forms
1 large triangle.
#### Step 3: Count all triangles.
- Total triangles = 7 (small) + 3 (medium) + 1 (large) =
11 triangles.
Thus, the total number of triangles in the second shape is
11.
---
Final Answers:
1. For the first shape:
5 triangles
2. For the second shape:
11 triangles
Boxed Answers:
\[
\boxed{5 \text{ and } 11}
\]
Parent Tip: Review the logic above to help your child master the concept of geometry puzzles printable.
