Triangle Interiors Quiz

Bisectors
Find the value for x and the length of DB. How can they be proven?
What is the measure of [math]\angle[/math]BAC? How do you know?
Centers
Where is the circumcenter located for the triangle with the given vertices? (inside, outside, or on the triangle)[br]X(−2, 1), Y(2,−3), Z(6,−3).
Find the coordinates of the centroid of the triangle with the given vertices.[br]A(−10, 3), B(−4, 5), C(−4, 1).
Plot the triangle with the vertices A(−6, 8), B(−6, 4), and C(0, 4).  Then plot its midsegment triangle.
Inequalities
Describe the possible lengths of the third side of the triangle if the lengths of the other two sides are 4 inches and 8 inches.
Given triangles RST and RQT share a side RT. If RQ = RS and m∠QRT>m∠SRT, then how does QT compare to ST?
Real world
A photographer is trying to take a picture of a large group, but can't fit everyone in the picture. Give at least two ways to address the problem and an explanation for why each one works.
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