Lemmas 1-5 and Basic Problems I-III
- Author:
- Kristen
Lemmas 1-5
Lemma 1: Given a line l and a point P no ton l, it is possible to construct a line m through P such that m || l using only a straightedge.
Lemma 2: Given a line l, a point P not on l, and a circle c with center O, it is possible to construct a line n through P such that nl using only a straightedge.
Lemma 3: Given a segment PQ, a point A, a direction, and a circle c with center O, it possible to construct a segment AS with length PQ in the given direction using only a straightedge.
Lemma 4: Given segments of length m, n, and s, it is possible to construct a segment of length using only a straightedge.
Lemma 5: Given segments of length a, b, and a circle c with center O, it is possible to construct a segment of length using only a straightedge.
Basic Problems I-III
Basic Problem I: To construct the intersection of two lines.
Basic Problem II: To construct the intersection of a line and a circle.
Basic Problem III: To construct the intersection of two circles.