Geometry Triangle Midsegment Theorem-Summer School

Front

What is the Triangle Midsegment Theorem?

Back

The Triangle Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

Front

If a triangle has sides of lengths 10, 14, and 18, what is the length of the midsegment connecting the midpoints of the sides of lengths 10 and 14?

Back

The length of the midsegment is half the length of the third side, which is 18. Therefore, the midsegment length is 9.

Front

What is the relationship between the midsegment and the third side of a triangle?

Back

The midsegment is parallel to the third side and its length is half of the third side.

Front

If the midsegment of a triangle is 7, what is the length of the third side?

Back

The length of the third side is 14, since the midsegment is half of the third side.

Front

How do you find the length of a midsegment in a triangle?

Back

To find the length of a midsegment, identify the lengths of the two sides it connects, and use the Triangle Midsegment Theorem to determine its relationship to the third side.

Front

If the lengths of two sides of a triangle are 8 and 6, what is the maximum possible length of the third side?

Back

The maximum possible length of the third side is less than the sum of the two sides, which is 14.

Front

What is the perimeter of a triangle with sides 12, 16, and 20?

Back

The perimeter is 12 + 16 + 20 = 48.

Front

If the midsegment of a triangle is 10, what can you say about the third side?

Back

The third side must be 20, as the midsegment is half the length of the third side.

Front

What is the significance of the midsegment in triangle similarity?

Back

The midsegment creates two smaller triangles that are similar to the original triangle, maintaining proportionality.

Front

If a triangle has a midsegment of length 5, what is the length of the side it is parallel to?

Back

The length of the side it is parallel to is 10.