document.write( "Question 446719: Please, help me, this is very confusing. Richard asked to re-post it with more info; this is all I have. Thanks Richard.
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\n" ); document.write( "Proof:
\n" ); document.write( "Statement 1: m Arc RX = 100. Reason 1: Given
\n" ); document.write( "Statement 2: m Ang RSX = ____. Reason 2: The measure of an inscribed angle is ½ the measure of the intercepted arc.
\n" ); document.write( "Statement 3: m Ang RSX = 50. Reason 3: Substitution
\n" ); document.write( "Statement 4: m Ang T = 50. Reason 4: Given
\n" ); document.write( "Statement 5: m Ang T = m Ang RSX. Reason 5: Substitution
\n" ); document.write( "Statement 6: Ang T = Ang RSX. Reason 6: Definition of congruent angles
\n" ); document.write( "Statement 7: RT is a tangent segment. Reason 7: Given
\n" ); document.write( "Statement 8: m Ang TRS = _____. Reason 8:An angle formed by a secant and a tangent is ___ the measure of its intercepted arc.
\n" ); document.write( "Statement 9: m Ang SXR = ½ m Arc RS. Reason 9:The measure of an inscribed angle is ½ the measure of the intercepted arc.
\n" ); document.write( "Statement 10: m Ang TRS = m Ang SXR. Reason 10: Substitution
\n" ); document.write( "Statement 11: Ang TRS = Ang SXR. Reason 11: Definition of congruent angles
\n" ); document.write( "Statement 12: Triangle RST is similar to Triangle XRS. Reason 12: ___ Similarity Theorem\r
\n" ); document.write( "\n" ); document.write( "Figure 1: Segment UX is a diameter, and segment TZ is a tangent. m Arc TX = 50, m Arc XW = 30, and m Arc UV = 20. Note: Ang 8 is Ang XTU, NOT Ang XTV.
\n" ); document.write( "Figure 2: PE and PF are tangent segments.
\n" ); document.write( "Figure 3: AT is a tangent segment, and AS is a secant segment.
\n" ); document.write( "Figure 4: Secants OA and OB and tangent OC are drawn from point O.
\n" ); document.write( "Figure 5: RT is a tangent segment, m Ang T = 50, and m Arc RX = 100.
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\n" ); document.write( " QUESTIONS
\n" ); document.write( "19: For the proof given above, what is missing in Statement #2?
\n" ); document.write( "20: For the proof given above, what is missing in Statement #8?
\n" ); document.write( "21: For the proof given above, what is missing in Reason #8?
\n" ); document.write( "22: For the proof given above, what is missing in Reason #12? \n" ); document.write( "

Algebra.Com's Answer #307680 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
I believe the third website is the only one used, since the others have irrelevant points/figures.\r
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\n" ); document.write( "\n" ); document.write( "19. Applying the fact that the inscribed angle is half the measure of the arc, angle RSX = 50.\r
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\n" ); document.write( "\n" ); document.write( "20, 21. The angle TRS is equal to one half the measure of the arc. Given this, we can say that angle TRS = (1/2)RS = angle SXR because they both cover the same arc (okay, I probably just said statement 9).\r
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\n" ); document.write( "\n" ); document.write( "22. Combining statements 6 and 11, we have established AA (two sets of congruent angles), implying AAA similarity. \n" ); document.write( "

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