need help with question 6. 1. În class we proved what we called the Trilateratio
ID: 3003704 • Letter: N
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need help with question 6.
1. În class we proved what we called the Trilateration Lemma, which says that if ?ABC and AA'B'C are congruent than any point P determines a unique point P' such that Show that if Q is another point, and it determines the point Q' via the correspondence above, then PQ P'Q. Use this to show that there is an isometry T that takes ???? to ??'B'C, and moreover, that it is unique: if S is an isometry that also takes ?ABC to . A'B'C, then S-T. 2. Suppose that T is an isometry and T2 -TT I, the identity isometry. Show that T must be a reflection about some line or a rotation around some point by 180°. 3. Given a line l, let Mi denote the reflection about I Suppose l and k are parallel lines. Describe exactly what MiMe does. Now suppose l and k are not parallel. What does MiMk do? 4. Suppose j, k, and l are concurrent lines that pass through the point O. Show that MyMkMi is a reflection about some line that also passes through . 5. Given a point P and an angle ?, let RPA denote the rotation around P clockwise by ?. Let A and B be distinct points. Describe the isometry RA/ARB.x/4 6. Suppose T is a rotation that takes the line segment AB to the line segment A'B. Show how you would locate the center of the rotation.Explanation / Answer
Connect the points A and A'. Draw the perpendicular bisector of AA'. Connect the points B and B'. Draw the perpendicular bisector of BB'. The point of intersection of both the perpendicular bisectors is the CENTER OF ROTATION.
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