By Mumford D., Fogarty J.

ISBN-10: 3540032843

ISBN-13: 9783540032847

ISBN-10: 3540112901

ISBN-13: 9783540112907

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**Extra resources for Geometric Invariant Theory**

**Sample text**

The midpoint bisects the segment, or divides the segment into two congruent segments. EXAMPLE Study the diagrams below. a. Name each midpoint and the segment it bisects. b. Name all the congruent segments. Use the congruence symbol to write your answers. Solution Look carefully at the markings and apply the midpoint definition. a. CF = FD, so F is the midpoint of CD; JK b. CF FD, HJ HL, and JK KL , so K is the midpoint of JL. KL. Even though EF and FG appear to have the same length, you cannot assume they are congruent without the markings.

Science Mathematician DeWitt Sumners at Florida State University and biophysicist Sylvia Spenger at the University of California, Berkeley, have discovered that when a virus attacks DNA, it creates a knot on the DNA. htm 8. The square knot and granny knot are very similar but do very different things. Compare their symmetries. Use string to re-create the two knots and explain their differences. 9. Cut a long strip of paper from a sheet of lined paper or graph paper. Tie the strip of paper snugly, but without wrinkles, into a simple knot.

23. If m D = 40° and m C = 140°, then angles C and D are a linear pair. 24. If point A is not the midpoint of CT , then CA AT. Review For Exercises 25 and 26, refer to the graph at right. 25. Find possible coordinates of a point P so that points P, T, and S are collinear. 26. Find possible coordinates of a point Q so that QR || TS. 27. A partial mirror reflects some light and lets the rest of the light pass through. In the figure at right, half the light from point A passes through the partial mirror to point B.

### Geometric Invariant Theory by Mumford D., Fogarty J.

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