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.
http://www.learningbygrace.org/geom/images/geom_26.3.1,2.jpg
http://www.learningbygrace.org/geom/images/geom_26.3,4.jpg
http://www.learningbygrace.org/geom/images/geom_26.3.5.jpg
Proof:
Statement 1: m Arc RX = 100. Reason 1: Given
Statement 2: m Ang RSX = ____. Reason 2: The measure of an inscribed angle is ½ the measure of the intercepted arc.
Statement 3: m Ang RSX = 50. Reason 3: Substitution
Statement 4: m Ang T = 50. Reason 4: Given
Statement 5: m Ang T = m Ang RSX. Reason 5: Substitution
Statement 6: Ang T = Ang RSX. Reason 6: Definition of congruent angles
Statement 7: RT is a tangent segment. Reason 7: Given
Statement 8: m Ang TRS = _____. Reason 8:An angle formed by a secant and a tangent is ___ the measure of its intercepted arc.
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.
Statement 10: m Ang TRS = m Ang SXR. Reason 10: Substitution
Statement 11: Ang TRS = Ang SXR. Reason 11: Definition of congruent angles
Statement 12: Triangle RST is similar to Triangle XRS. Reason 12: ___ Similarity Theorem
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.
Figure 2: PE and PF are tangent segments.
Figure 3: AT is a tangent segment, and AS is a secant segment.
Figure 4: Secants OA and OB and tangent OC are drawn from point O.
Figure 5: RT is a tangent segment, m Ang T = 50, and m Arc RX = 100.
QUESTIONS
19: For the proof given above, what is missing in Statement #2?
20: For the proof given above, what is missing in Statement #8?
21: For the proof given above, what is missing in Reason #8?
22: For the proof given above, what is missing in Reason #12?
Answer by richard1234(7193)   (Show Source):
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.
19. Applying the fact that the inscribed angle is half the measure of the arc, angle RSX = 50.
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).
22. Combining statements 6 and 11, we have established AA (two sets of congruent angles), implying AAA similarity.
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