Geometry warm-up exercise on triangle medians and properties.

I'll solve the geometry problems presented in the image step by step.

Problem 1: If CD = 3.25, what is BC?

Since AD is a median, it connects vertex A to the midpoint D of side BC.
- By definition, a median divides the opposite side into two equal segments.
- Therefore, BD = CD
- So BC = BD + CD = CD + CD = 2 × CD
- BC = 2 × 3.25 = 6.5

Problem 2: Find AG if DG = 10

The point G is the centroid of triangle ABC (the intersection of the medians CE and AD).
- A key property of the centroid is that it divides each median in a 2:1 ratio, with the longer segment being closer to the vertex.
- For median AD, this means AG:GD = 2:1
- Since DG = 10, then AG = 2 × DG = 2 × 10 = 20

Problem 3: If CG = 7, find CE

Again, G is the centroid, which divides median CE in a 2:1 ratio.
- This means CG:GE = 2:1
- Since CG = 7, then GE = CG/2 = 7/2 = 3.5
- Therefore, CE = CG + GE = 7 + 3.5 = 10.5

Classification of lines in triangles

The image shows four different scenarios:

1. Altitude: A line from a vertex perpendicular to the opposite side (marked with a right angle symbol).
2. Neither: A line that is neither perpendicular to the opposite side nor bisects it.
3. Both: A line that is both an altitude (perpendicular) and a bisector (divides the side into two equal parts, marked with tick marks).
4. Perpendicular Bisector: A line that is perpendicular to a side and also bisects it (shown with right angle symbol and tick marks on both segments).

These classifications are correct based on standard geometric definitions.

All answers match the red text provided in the image, confirming they are correct.