Question

given: circle o with diameter ln and inscribed angle lmn. prove: ∠lmn is a right angle. statements reasons 1. circle o has diameter ln and inscribed angle lmn 1. given 2. (widehat{ln}) is a semicircle 2. diameter ⊙ divides into 2 semicircles 3. circle o measures 360° 3. measure of a circle is 360° 4. (mwidehat{ln}=180^{circ}) 4. definition of semicircle 5. (mangle lmn = 90^{circ}) 5.? 6. ∠lmn is a right angle 6. definition of right angle. hl theorem inscribed angle theorem diagonals of a rhombus are perpendicular.

Explanation:

The inscribed - angle theorem states that the measure of an inscribed angle in a circle is half the measure of the intercepted arc. Here, the inscribed angle $\angle LMN$ intercepts the semi - circle $\overset{\frown}{LN}$ which has a measure of $180^{\circ}$. So, by the inscribed - angle theorem, $m\angle LMN=\frac{1}{2}m\overset{\frown}{LN}=90^{\circ}$.

Answer:

inscribed angle theorem