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so today Im going to be teaching you about several important relationships that follow directly from the inscribed angle theory so the first example is if two inscribed angles intercept the same or congruent arcs then the angles are congruent so in the accompanying figure inscribed angles B and D are congruent because they intercept the same arc AC so for the second example or corollary to an angle inscribed in a semi-circle is a right angle so in the income can figure because angle a HB is inscribed in a semi-circle its intercepted arcs is also a semicircle so onto corollary three the opposite angles of inscribed quadrilaterals are supplementary so in the accompanying figure angles a and alc are supplementary going with that angles B and D are also supplementary angles