📐 geometry

1. **State the problem:** Determine if the lengths 2.3, 1.5, and 3.4 can form a triangle. 2. **Recall the triangle inequality theorem:** For any triangle with sides $a$, $b$, and $

1. The problem asks if a triangle can have sides of lengths 17.5, 18.8, and 5.7. 2. To determine this, we use the Triangle Inequality Theorem, which states that for any triangle wi

1. **Problem statement:** We have a triangle with two sides of lengths 6 and 1. We want to find the smallest possible whole-number length for the third side. 2. **Formula and rule:

1. **State the problem:** Determine if a triangle can be formed with side lengths 14.4, 11.9, and 4.8. 2. **Formula and rule:** For any triangle with sides $a$, $b$, and $c$, the t

1. **Problem statement:** We have a triangle with two sides of lengths 17 and 19. We want to find the largest possible whole-number length for the third side. 2. **Formula and rule

1. The problem asks if a triangle can have sides of lengths 0.8, 6.9, and 7.7. 2. To determine this, we use the Triangle Inequality Theorem, which states that for any triangle with

1. The problem asks if a triangle can have sides of lengths 3, 7, and 9. 2. To determine this, we use the Triangle Inequality Theorem, which states that for any triangle with sides

1. The problem asks if a triangle can have side lengths 1, 2, and 3. 2. To determine this, we use the Triangle Inequality Theorem, which states that for any triangle with sides $a$

1. **State the problem:** We need to determine if the lengths 0.2, 6.3, and 6.5 can form a triangle. 2. **Recall the triangle inequality theorem:** For any triangle with sides $a$,

1. The problem asks if a triangle can have sides of lengths 1, 9, and 9. 2. To determine this, we use the triangle inequality theorem, which states that for any triangle with sides

1. **State the problem:** Determine if a triangle can have side lengths 3, 7, and 10. 2. **Recall the triangle inequality theorem:** For any triangle with sides $a$, $b$, and $c$,

1. **State the problem:** We are given a triangle \(\triangle STV\) with a midsegment \(RU\). The length of side \(ST\) is \(z\), and the length of the midsegment \(RU\) is \(z - 1

1. **State the problem:** We are given triangle $QSU$ with $RT$ as the midsegment connecting the midpoints of sides $QU$ and $US$. We know $QU = w + 49$ and $RT = w + 17$. We need

1. **State the problem:** We are given a triangle WUY with points V and X as midpoints of segments UW and WY respectively.

1. **State the problem:** We are given a triangle \(\triangle STV\) with \(UW\) as the midsegment parallel to side \(ST\). The lengths are given as \(ST = p - 64\) and \(UW = p - 8

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