Geometry

Given the map scale is 1 cm = 50 km, and the distance on the map between two places is 3 cm, we can calculate the actual distance.

Calculation:

• Map distance: 3 cm
• Scale: 1 cm = 50 km

Multiply the map distance by the scale factor:
3 cm * 50 km/cm = 150 km

Answer: The actual distance between the two locations is 150 km.

To provide an accurate answer, I need more context. The phrase "the four flags following what diagram?" is missing information. Please provide the name or a description of the diagram you are referring to.

For example, you could be referring to a:

• Specific chart
• Visual representation
• Map
• Technical drawing

The Basic Proportionality Theorem, also known as Thales' Theorem, states the following:

Theorem: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

In simpler terms:

Consider a triangle ABC. If a line DE is drawn parallel to BC, where D is a point on AB and E is a point on AC, then the theorem states that:

AD/DB = AE/EC

Converse of the Basic Proportionality Theorem:

The converse of the theorem is also true. It states:

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

An obtuse angle bisector refers to a line or ray that divides an obtuse angle into two equal angles. Here's a breakdown:

• Obtuse Angle: An obtuse angle is an angle that measures greater than 90 degrees and less than 180 degrees.
• Angle Bisector: An angle bisector is a line or ray that divides an angle into two congruent (equal) angles.

Therefore, when you bisect an obtuse angle, you are creating two acute angles (angles less than 90 degrees).

For example, if you have an obtuse angle of 120 degrees, its bisector will divide it into two angles of 60 degrees each.

The volume of a cube is calculated by cubing the length of one of its sides. In other words, Volume = side * side * side.

Given a cube with sides of 3cm, the volume is:

Volume = 3cm * 3cm * 3cm = 27cm³

Therefore, the volume of the cube is 27 cubic centimeters.