2. Prove three of the following four theorems from hyperbolic geometry. If point

Question

2. Prove three of the following four theorems from hyperbolic geometry. If points A, B, C are equidistant from a line m, then the three points are not collinear. The measure of an exterior angle of a triangle is greater than the sum of the measures of the two opposite interior angles. a. b. c. If k is sensed parallel to n, P is a point on k and Q is a point on n such that the segment PQ is perpendicular to n, S is a point on segment PQ (but not P or Q), and is a line perpendicular to PQ at S, then intersects k. The length of the line joining the midpoints of two sides of a triangle is less than half the length of the other side. (Only prove this for the case where all angles are acute as shown in the diagram below.) d.

Explanation / Answer

Part C

k , n are two lines sensed to be parallel to eachother. P is a point on line k and Q is a point in line n such that PQ is perpendicular to n. Also, l is a line perpendicular to PQ at S.

We can conclude that, lines l and n are parallel to each other.
Since k is not parallel to n, it can't be parallel to l.. since line l || line n

At some point, line l will intersect k

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.