Question

We are given △ABC and point D such that A−D-B. We have cevian DB . We also are given m∠CAB= (π/7) and mxABC=(6π/11). 1. Use the Exterior Angle inequality to establish upper and lower bounds for mCDB. Prove your resulting inequality. 2. Construct the figures above as general dynamic figures in Euclidean Geometry. Make the control points A, B, and D. Verify your solution in part A for this triangle by measuring. 3. Construct the figures above as general dynamic figures in Hyperbolic Geometry. Make the control points A, B, and D. Verify your solution in part A for this triangle by measuring.

Answer 1

The given information does not allow us to establish upper and lower bounds for ∠CDB using the Exterior Angle inequality.

Step-by-step explanation:

To establish upper and lower bounds for mCDB, we can use the Exterior Angle inequality. According to this inequality, the measure of an exterior angle of a triangle is greater than the measure of either of its non-adjacent interior angles. In this case, m∠CAB is the exterior angle, and m∠ABC is one of the non-adjacent interior angles.

Therefore, we can establish the following inequality:

m∠CAB > m∠ABC

Since we are given m∠CAB = (π/7) and mxABC=(6π/11), we can substitute these values into the inequality:

(π/7) > (6π/11)

Now, we can simplify the inequality:

11π > 42π

Dividing both sides by π, we get:

11 > 42

This is a false statement, so the inequality is not true. Therefore, we cannot establish upper and lower bounds for mCDB using the given information.