basicelements of differential geometry and topology

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VZ and XY are the opposite sides of a rectangle. 2. The opposite sides of a rectangle are congruent. Conclusion: VZ =' XY zvl ------~ In Exercises 23-28, write the correct conclusion. 23. 1. The opposite sides of a parallelogram are parallel. 2. VX and ZY are opposite sides of parallelogram VXYZ. Conclusion: _1_ 24. 1. Two intersecting lines determine exactly one plane. 2. Lines p and q intersect. Conclusion: _1_ 25. 1. Two coplanar lines either intersect or are parallel. 2. Coplanar lines p and q do not intersect.

20. It measures less than 90. 21. Coplanar points are in the same plane. 22. A triangle is when you have three angles and three sides. 23. Congruent segments are segments that have the same measure and are equal. 24. An angle is a geometric figure. C I 25. Rewrite the statements in Exercises 19-24 so that they are acceptable definitions. PV~~&B-----------Five blocks are placed in a row as shown below. Each block is covered with paper showing 6 pictures arranged the same way on each block. If a paper cover is removed and flattened out as shown below on the right.

How many Jines can you draw through 6 points? ) Segments and Angles 45 onstructions Constructing a Segment Congruent to a Given Segment /\ In constructions. a straightedge is used to draw lines, segments, or rays A straightedge looks like a ruler without measurement marks A compass is used in constructions to draw circles or arcs of circles. A circle is the set of all points in a plane that are at a given distance from a given point in the plane. The given point is the center of the circle and the given distance is the radius.

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