Algebraic Geometry

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By D. Mumford

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62. H E 63. 5 ]› In each diagram, BD bisects ∠ ABC. Find m∠ ABD and m∠ DBC. (p. 24) 1. 2. (x 1 20)8 A D A C (10x 2 42)8 (6x 1 10)8 (3x 2 4)8 B B 3. A (18x 1 27)8 D (9x 1 36)8 D B C C Find the measure of (a) the complement and (b) the supplement of ∠ 1. (p. 35) 4. m∠ 1 5 478 5. 5, p. 897 6. m∠ 1 5 758 7. 6 Before Now Why? Key Vocabulary • polygon side, vertex • convex • concave • n-gon • equilateral • equiangular • regular Classify Polygons You classified angles. You will classify polygons. So you can find lengths in a floor plan, as in Ex.

41. 24 22 230 ★ 220 36. 0 2 210 39. 0 37. 28 26 24 22 29 26 0 2 4 40. 23 0 3 220 210 0 28 24 26 10 20 22 30 0 MULTIPLE CHOICE The endpoints of } LF are L(22, 2) and F(3, 1). The endpoints of } JR are J(1, 21) and R(2, 23). What is the approximate difference in the lengths of the two segments? 24 42. 96 } } SHORT RESPONSE One endpoint of PQ is P(22, 4). The midpoint of PQ is M(1, 0). Explain how to find PQ. COMPARING LENGTHS The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent.

B E F A D C ★ MULTIPLE CHOICE Which is a correct name for the obtuse angle in the diagram? A ∠ ACB B ∠ ACD C ∠ BCD D ∠C B A C D EXAMPLE 3 ANGLE ADDITION POSTULATE Find the indicated angle measure. on p. 26 for Exs. 22–27 22. m∠ QST 5 ? 23. m∠ ADC 5 ? 24. m∠ NPM 5 ? P T 218 528 478 P M 798 448 N C B S L D A R ALGEBRA Use the given information to find the indicated angle measure. 25. Given m∠ WXZ 5 808, find m∠ YXZ. 26. Given m∠ FJH 5 1688, find m∠ FJG. X W G (x 1 5)8 (6x 2 15)8 (3x 2 5)8 Y 27. F J Z (x 1 8)8 H ★ MULTIPLE CHOICE In the diagram, the measure of ∠ XYZ is 1408.

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