Question

prove: ∠lmn is a right angle. 1. circle o has diameter ln and inscribed angle lmn 1. given 2. \\(\overarc{lkn}\\) is a semicircle 2. diameter ⊙ divides into 2 semicircles 3. circle o measures \\(360^\circ\\) 3. measure of a circle is \\(360^\circ\\) 4. \\(m\overarc{lkn} = 180^\circ\\) 4. definition of semicircle 5. \\(m\angle lmn = 90^\circ\\) 5.? 6. ∠lmn is a right angle 6. definition of right angle \\(\bigcirc\\) hl theorem \\(\bigcirc\\) inscribed angle theorem \\(\bigcirc\\) diagonals of a rhombus are perpendicular. \\(\bigcirc\\) ∠ formed by a tangent and a chord is half the measure of the intercepted arc. mark this and return save and exit next submit

Explanation:

To justify that $m\angle LMN = 90^\circ$, we use the rule that an inscribed angle intercepting a semicircle is half the measure of its intercepted arc. The intercepted arc $\overparen{LKN}$ is $180^\circ$, so the inscribed angle is $\frac{1}{2} \times 180^\circ = 90^\circ$, which comes from the inscribed angle theorem.

Answer:

inscribed angle theorem