Congruent Proof Theorem

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Congruent Proof Theorem

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Given: ∟Y and ∟RST are supplementary to ∟XSZ, XY TS, ∟RTS ∟RXY Prove: RX bisects ∟YRT |dw:1327192324410:dw|
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First note that the measure of angle XST + Measure of angle XSZ form a straight line and therefore have a sum of 180 degrees. We can then state that angle XST is supplementary to angle XSZ. This indicates that angle XST is congruent to angle Y which is also supplementary to angle XSZ. We now can state that the triangles RXY and RTS are Congruent using Angle - Side - Angle. Since the Triangles are congruent, the corresponding parts are congruent. This means that angle YRX is congruent to angle XRT which indicates that RX is a bisector of the angle YRT..

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