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14. In this exercise, we will review several basic Euclidean construc- tions with a straightedge and compass. Such constructions fasci- nated mathematicians from ancient Greece until the nineteenth cen- tury, when all classical construction problems were finally solved. (a) Given a segment AB. Construct the perpendicular bisector of AB. (Hint: Make AB a diagonal of a rhombus, as in Figure 1.23.) (b) Given a line l and a point P lying on l. Construct the line through P perpendicular to l. (Hint: Make P the midpoint of a segment of 1.) (c) Given a linel and a point P not lying on l. Construct the line through P perpendicular to l. (Hint: Construct isosceles trian- gle AABP with base AB on l and use (a).) (d) Given a line l and a point P not lying on l. Construct a line through P parallel to l. (Hint: Use (b) and (c).) (e) Construct the bisecting ray of an angle. (Hint: Use the Euclid- ean theorem that the perpendicular bisector of the base on an A B

14. In this exercise, we will review several basic Euclidean construc- tions with a straightedge and compass. Such constructions fasci- nated mathematicians from ancient Greece until the nineteenth cen- tury, when all classical construction problems were finally solved. (a) Given a segment AB. Construct the perpendicular bisector of AB. (Hint: Make AB a diagonal of a rhombus, as in Figure 1.23.) (b) Given a line l and a point P lying on l. Construct the line through P perpendicular to l. (Hint: Make P the midpoint of a segment of 1.) (c) Given a linel and a point P not lying on l. Construct the line through P perpendicular to l. (Hint: Construct isosceles trian- gle AABP with base AB on l and use (a).) (d) Given a line l and a point P not lying on l. Construct a line through P parallel to l. (Hint: Use (b) and (c).) (e) Construct the bisecting ray of an angle. (Hint: Use the Euclid- ean theorem that the perpendicular bisector of the base on an A B

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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14. In this exercise, we will review several basic Euclidean construc- tions with a straightedge and compass. Such constructions fasci- nated mathematicians from ancient Greece until the nineteenth cen- tury, when all classical construction problems were finally solved. (a) Given a segment AB. Construct the perpendicular bisector of AB. (Hint: Make AB a diagonal of a rhombus, as in Figure 1.23.) (b) Given a line l and a point P lying on l. Construct the line through P perpendicular to l. (Hint: Make P the midpoint of a segment of l.) (c) Given a line l and a point P not lying on l. Construct the line through P perpendicular to l. (Hint: Construct isosceles trian- gle AABP with base AB on l and use (a).) (d) Given a line l and a point P not lying on l. Construct a line through P parallel to l. (Hint: Use (b) and (c).) (e) Construct the bisecting ray of an angle. (Hint: Use the Euclid- ean theorem that the perpendicular bisector of the base on an A B
Transcribed Image Text:14. In this exercise, we will review several basic Euclidean construc- tions with a straightedge and compass. Such constructions fasci- nated mathematicians from ancient Greece until the nineteenth cen- tury, when all classical construction problems were finally solved. (a) Given a segment AB. Construct the perpendicular bisector of AB. (Hint: Make AB a diagonal of a rhombus, as in Figure 1.23.) (b) Given a line l and a point P lying on l. Construct the line through P perpendicular to l. (Hint: Make P the midpoint of a segment of l.) (c) Given a line l and a point P not lying on l. Construct the line through P perpendicular to l. (Hint: Construct isosceles trian- gle AABP with base AB on l and use (a).) (d) Given a line l and a point P not lying on l. Construct a line through P parallel to l. (Hint: Use (b) and (c).) (e) Construct the bisecting ray of an angle. (Hint: Use the Euclid- ean theorem that the perpendicular bisector of the base on an A B
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