1. The problem asks: How many triangles are in the given geometric sketch? 2. The sketch is a large rectangle divided into 3 rows and 3 columns, making 9 smaller rectangles. 3. Each row has a diagonal line creating triangles within those smaller rectangles. 4. Let's analyze each row separately: - Top row: The diagonal runs from the top right corner to the middle of the row, splitting the top three rectangles into triangles. - Middle row: The diagonal runs from the middle of the left edge to the right middle, splitting the middle three rectangles. - Bottom row: The diagonal runs from the left middle to the bottom right corner, splitting the bottom three rectangles. 5. Each diagonal in a rectangle creates 2 triangles. 6. Since there are 3 rectangles per row and 3 rows, total rectangles = $3 \times 3 = 9$. 7. Each rectangle has 1 diagonal line creating 2 triangles, so total triangles = $9 \times 2 = 18$. 8. Therefore, the total number of triangles in the sketch is $18$. Final answer: $18$ triangles.