Mid-Segment Theorem: Real-World Geometry Challenges

A triangle has a mid-segment that measures 8 cm. If the base of the triangle is 20 cm, what is the length of the other side of the triangle?

• The other side is 12 cm.

• The other side is 16 cm.

• The other side is 10 cm.

• Cannot be determined with the given information.

In a triangle, the mid-segment is 12 cm long. If the lengths of the two sides it connects are 30 cm and 36 cm, what is the relationship between these lengths and the mid-segment?

• The mid-segment is equal to the longer side.

• The mid-segment is greater than the shorter side.

• The mid-segment is less than the average of the two sides it connects.

• The mid-segment is the average of the two sides.

A park is designed in the shape of a triangle. The mid-segment connecting two sides measures 15 m. If the lengths of the two sides are 30 m and 36 m, how does the mid-segment help in determining the area of the park?

• The mid-segment measures the angle between the two sides.

• The mid-segment is irrelevant to the area calculation.

• The mid-segment helps in determining the area of the park by providing a reference for the height when calculating the area of the triangle.

• The mid-segment indicates the perimeter of the triangle.

A triangular garden has a mid-segment that is 10 ft long. If the two sides it connects are 24 ft and 28 ft, what is the length of the third side of the triangle?

• 22 ft

• 18 ft

• 26 ft

• 20 ft

In a triangle, the mid-segment is 5 inches long. If the lengths of the two sides it connects are 12 inches and 14 inches, what can you conclude about the triangle's dimensions?

• The triangle's dimensions are consistent with the properties of mid-segments.

• The triangle's dimensions are inconsistent with the properties of mid-segments.

• The mid-segment is longer than both sides it connects.

• The triangle is equilateral with all sides equal.

A triangular roof has a mid-segment that measures 9 ft. If the base of the roof is 24 ft, what is the length of the other side of the roof?

• 12 ft

• 18 ft

• 21 ft

• 15 ft

A triangular plot of land has a mid-segment of 7 m. If the lengths of the two sides it connects are 14 m and 18 m, what is the relationship between the mid-segment and the sides?

• The mid-segment is equal to the sum of the two sides.

• The mid-segment is less than the average of the two sides.

• The mid-segment is greater than the longer side.

• The mid-segment is the average of the two sides.

In a triangle, the mid-segment measures 6 cm. If the lengths of the two sides it connects are 16 cm and 20 cm, how can you use the mid-segment to find the perimeter of the triangle?

• 36 cm

• 40 cm

• 48 cm

• 52 cm

A triangular swimming pool has a mid-segment of 11 m. If the lengths of the two sides it connects are 22 m and 26 m, what is the length of the third side of the triangle?

• 15 m

• 20 m

• 24 m

• 18 m

A triangular piece of land has a mid-segment that measures 4 m. If the lengths of the two sides it connects are 10 m and 12 m, what can you infer about the dimensions of the triangle?

• The dimensions of the triangle are 10 m, 12 m, and 6 m.

• The dimensions of the triangle are 10 m, 12 m, and 8 m.

• The dimensions of the triangle are 8 m, 10 m, and 12 m.

• The dimensions of the triangle are 4 m, 10 m, and 12 m.