📐 geometry

1. **Problem statement:** Given that QS is a midsegment of triangle PRT, and the lengths PT = $x + 54$ and QS = $x + 25$, find the value of $x$. 2. **Recall the midsegment theorem:

1. **Problem Statement:** We are given a triangle $\triangle VXZ$ with $WY$ as a midsegment. The segment $VZ$ has length $p$, and the midsegment $WY$ has length $p - 14$. We need t

1. **Problem Statement:** We are given triangle $\triangle VXZ$ with $WY$ as a midsegment. We know $VZ = p$ and $WY = p - 14$. We need to find the value of $p$. 2. **Key Concept:**

1. **Problem statement:** Given that SU is a midsegment of triangle \(\triangle RTV\), and \(RV = p\), \(SU = p - 15\), find the value of \(p\). 2. **Recall the midsegment theorem:

1. **State the problem:** We are given two expressions for line segments in a quadrilateral: $UV = x - 61$ and $TW = x - 63$. We need to find the value of $x$. 2. **Analyze the pro

1. **Problem statement:** Given triangle VYX with W and Z as midpoints of segments VX and VY respectively, and segment WZ = 10, find the length of XY. 2. **Key concept:** When W an

1. **Problem Statement:** We have a right triangle $VXY$ with a right angle at $V$. Points $W$ and $Z$ are midpoints of segments $VX$ and $VY$ respectively. Given that $WZ = 10$, w

1. **State the problem:** We have a large right triangle VYX and a smaller triangle WZX inside it. W is the midpoint of VX, and Z is the midpoint of VY. Given that the length WZ =

1. **Problem statement:** Given triangle $\triangle UVX$ with $TW$ as a midsegment parallel to side $UX$, and $UV = 54$, find the length of $TW$. 2. **Key property:** A midsegment

1. **State the problem:** We are given triangle $\triangle QST$ with $RU$ as a midsegment. We know the length of side $ST = 8$, and we need to find the length of the midsegment $RU

1. **Problem statement:** Given triangle $PRS$ with $QT$ as the midsegment parallel to side $RS$, and $QT = 19$, find the length of $RS$. 2. **Formula and rule:** The midsegment th

1. **Problem Statement:** Given that SU is a midsegment of triangle \(\triangle RTV\) and \(RV = 10\), find the length of \(SU\). 2. **Key Concept:** A midsegment in a triangle con

1. **Problem Statement:** Given triangle RQT, S is the midpoint of segment RT, and U is the midpoint of segment QT. If the length of QR is 92, find the length of segment SU.

1. The problem asks to identify the term that describes the segment HJ in triangle HIG, given that it splits the angle at vertex H into two angles of 39° and 36°. 2. Important defi

1. The problem asks to identify the term that describes the segment $UW$ in triangle $VUT$ with point $W$ on side $VT$. 2. Definitions:

1. The problem states that \overline{UV} \cong \overline{VW}, meaning segments UV and VW are congruent. 2. We are asked to identify the term that describes \overline{XV} given the

1. The problem asks to identify the term that describes the segment VX in triangle UVW with point X inside such that angles UVX and WVX are both 32°. 2. Given that angles UVX and W

1. The problem states that \(\angle CED\) is a right angle, meaning it measures 90 degrees. 2. We are asked to identify which term describes segment \(CE\) given this information.

1. The problem asks to identify the term that describes segment WU in triangle WVT given the angles at vertex W. 2. Definitions:

1. **Problem Statement:** We are asked to identify the term that describes the line segment $\overline{SV}$ in the given polygon with vertices $R, V, U, S, T$. The polygon has a ri

1. The problem asks to identify the term that describes segment WY in triangle VUX with a right angle at W. 2. Given that WY is drawn from vertex W perpendicular to side UX, it for