For the following problems, you can use the definition of a convex polygon, and

Question

For the following problems, you can use the definition of a convex polygon, and any results from Chapters 3 and 4. Don't use theorems from Chapters 8 or 9. With the correct theorem from Chapter 3 and 4, each step below should be short. 1. Let ABCD be a convex quadrilateral. In the following, you will show that the diagonals AC and BD intersect. (a) Prove that AB * AC * AD: that is. the ray containing the diagonal AC is between the rays containing the adjacent sides AB and AD. (b) Using part (a), prove that B and D are on opposite sides of AC, and therefore the diagonal BD must intersect the line AC. (c) An identical argument establishes that the diagonal AC must intersect the line BD Given this, conclude that AC and BD intersect.

Explanation / Answer

Theorem 3.43 (Properties of Sides of Lines).Suppose`is a line.
(a) Both sides of`are nonempty sets.
(b) IfAandBare distinct points not on`, then A and Bare on opposite sides of if and only if AB

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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