To find the length of side PQ of triangle PQR when triangle STU is formed by connecting the midpoints of PQR's sides, simply double the length of the corresponding side of STU.
To determine the length of side PQ of triangle PQR given that triangle STU is formed by connecting the midpoints of the sides of triangle PQR, and knowing the lengths of the sides of triangle STU, we can use the properties of similar triangles and the fact that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
In other words, if STU is formed by connecting the midpoints of PQR, then each side of STU is half the length of the corresponding side of PQR.
Therefore, to find the length of PQ, you would simply take the length of the corresponding side of STU and multiply it by two.
Let's denote the midpoints of the sides of triangle PQR as A, B, and C. Then, the midpoints are as follows:
- Midpoint of PQ: A
- Midpoint of QR: B
- Midpoint of PR: C
Now, we form triangle STU with these midpoints:
- Side ST is formed by connecting midpoints B and C.
- Side SU is formed by connecting midpoints A and B.
- Side TU is formed by connecting midpoints A and C.
Given that the lengths of sides ST, SU, and TU are known, we need to determine the length of side PQ.
Complete Question:
Triangle STU is formed by connecting the midpoints of the side of triangle PQR. The lengths of the sides of triangle STU are shown. What is the length of overline PQ Figures not necessarily drawn to scale.