the figure shows eight congruent triangles. redraw the figure with four fewer segaments, so that only four congruent triangles remain.
Copy the figure in pencil, then experiment with erasing lines. Try erasing the top two and bottom two lines, or lines on the inside.
To redraw the figure with four fewer segments, we need to remove two segments that divide each of the eight congruent triangles into two smaller congruent triangles. Here's how you can do it:
1. Begin by drawing a large equilateral triangle as the base of the figure.
2. Divide each side of the equilateral triangle into three equal segments. This will create four smaller equilateral triangles within the larger one.
3. Next, remove one of the segments (either the top or bottom one) from each of the four smaller equilateral triangles. This removes four segments in total.
4. The remaining segments will form the sides of the four congruent triangles within the figure.
Here's a step-by-step breakdown of the process:
Step 1: Draw a large equilateral triangle as the base.
```
A
/ \
/ \
/_____\
B C
```
Step 2: Divide each side into three equal segments.
```
A
/ \
/ \
/____ \
/ \ / \
/ \ / \
B____C_____D
```
Step 3: Remove one segment from each of the smaller equilateral triangles.
```
A
/ \
/ \
/_____\
/ | \
/ | \
B_____|_____D
```
Step 4: The remaining segments form the sides of four congruent triangles.
```
A
/ \
/ \
/_____\
/ \
/_________\
B E D
```
In this redrawn figure, there are only four congruent triangles remaining, and four fewer segments compared to the original figure.