How are the semicircle and the diameter of a circle related? The length of the diameter and the length of semicircle are the same. The degree measure of the diameter and the degree measure of the semicircle are the same. The angle measure of the diameter is twice the angle measure of the semicircle.

Let's evaluate each of the statements to understand the relationship between a semicircle and the diameter of a circle. 1. **The length of the diameter and the length of the semicircle are the same.** - **False.** - **Diameter (d):** The length of the diameter of a circle is \( d = 2r \), where \( r \) is the radius. - **Semicircle Length:** The length of a semicircle is half the circumference of the circle, which is \( \frac{1}{2} \times 2\pi r = \pi r \). - **Comparison:** Unless \( 2r = \pi r \) (which only holds if \( r = 0 \), a trivial case), the lengths are not equal. Therefore, this statement is incorrect. 2. **The degree measure of the diameter and the degree measure of the semicircle are the same.** - **True.** - **Diameter:** When considering the angle subtended by the diameter at the center of the circle, it measures \( 180^\circ \) (a straight angle). - **Semicircle:** The angle subtended by a semicircle at any point on the circumference of the circle is also \( 180^\circ \). - **Conclusion:** Both have the same degree measure of \( 180^\circ \), making this statement correct. 3. **The angle measure of the diameter is twice the angle measure of the semicircle.** - **False.** - As established, both the diameter and the semicircle subtend an angle of \( 180^\circ \). - Therefore, the angle measure of the diameter is **not** twice that of the semicircle; they are equal. **Summary:** - **Only the second statement is correct.** The diameter and the semicircle both subtend an angle of \( 180^\circ \).