Question
Copy Segment BA to make Segment CD so that Segment CD is congruent (the same size as) BA. You will need to click on the circle tool, then select the "Circle by Length" button to get the "Compass Tool" to copy the radius of Circle B (segment BA). To copy segment BA, just click on it with the compass tool and drag it to point C to make Circle C.
Once Circle C is constructed, you can construct segment CD anywhere in Circle C. To label point D, click on the Arrow Select Tool, click on the point and then on the tab with the letter "A" to label.
How do you know CD is congruent (an exact copy) of BA?
Once Circle C is constructed, you can construct segment CD anywhere in Circle C. To label point D, click on the Arrow Select Tool, click on the point and then on the tab with the letter "A" to label.
How do you know CD is congruent (an exact copy) of BA?
Answers
GPT-4o mini
To confirm that segment CD is congruent to segment BA, you can use the following reasoning based on the construction steps taken:
1. **Circle Construction**: When you created Circle C using the compass tool, you copied the radius of Circle B (which is segment BA) directly onto Circle C. This means that the length of radius of Circle C is equal to the length of segment BA.
2. **Distance from Center**: Since CD lies anywhere within Circle C, the distance from the center of Circle C to point D matches the radius established when Circle C was constructed. Therefore, the length of segment CD is equal to the radius of Circle C.
3. **Definition of Congruence**: By definition, two segments are congruent if they have the same length. Since CD was created with the same radius as BA derived from Circle B, the lengths are identical. Thus, CD is congruent to BA.
4. **Verification**: If needed, you can use a ruler or measurement tool to confirm that the length of segment CD is the same as segment BA, reinforcing the conclusion that they are indeed congruent.
By following these points, you establish that segment CD is an exact copy of segment BA, confirming their congruence.
1. **Circle Construction**: When you created Circle C using the compass tool, you copied the radius of Circle B (which is segment BA) directly onto Circle C. This means that the length of radius of Circle C is equal to the length of segment BA.
2. **Distance from Center**: Since CD lies anywhere within Circle C, the distance from the center of Circle C to point D matches the radius established when Circle C was constructed. Therefore, the length of segment CD is equal to the radius of Circle C.
3. **Definition of Congruence**: By definition, two segments are congruent if they have the same length. Since CD was created with the same radius as BA derived from Circle B, the lengths are identical. Thus, CD is congruent to BA.
4. **Verification**: If needed, you can use a ruler or measurement tool to confirm that the length of segment CD is the same as segment BA, reinforcing the conclusion that they are indeed congruent.
By following these points, you establish that segment CD is an exact copy of segment BA, confirming their congruence.