📐 geometry

1. **State the problem:** Given that segment $ST \cong SN$ and angle $\angle 1 \cong \angle 2$, prove that triangles $\triangle STY$ and $\triangle SNX$ are congruent. 2. **Identif

1. **Problem statement:** Lily wants to paint her bedroom walls and ceiling. The room measures 4 m (length) × 3.5 m (width) × 2.5 m (height). There is a door (0.8 m × 2 m) and a wi

1. **Problem statement:** Delma wants to estimate the distance across a river by using her walking stick AB and sighting points T (tree across the river) and R (rock on her side).

1. The problem is to find the volume of a trapezoidal prism with bases 9.4 cm and 5.2 cm, height 6 cm, and length 205 mm. 2. First, convert all measurements to the same unit. Since

1. The problem asks us to determine if given triangles are congruent, identify which triangles are congruent, and state the postulate that proves their congruency. 2. To prove tria

1. **State the problem:** We are given that T is the midpoint of segment $\overline{WR}$ and two triangles $\triangle AWT$ and $\triangle ETR$ with certain congruent sides. We need

1. The problem states: Given the semicircles with radii 35 meters and 42.5 meters, and an angle of 100° between two line segments of lengths 20 inches and 12.5 inches, solve questi

1. **State the problem:** Calculate the volume $V$ of a rectangular prism with length $L=7.5$, width $W=2$, and height $H=15$. 2. **Formula:** The volume of a rectangular prism is

1. **State the problem:** Riley and Anthony run around a semi-circular curve. Riley runs on the inside lane with radius $35$ meters, and Anthony runs on the outside lane with radiu

1. **State the problem:** We need to find the length of a rectangular prism given its volume and two dimensions: height and width.

1. **State the problem:** We need to find how much area of the room will NOT be covered by the rug. 2. **Identify given information:** From the image annotations, the room's total

1. **Problem statement:** We have four rectangles A, B, C, and D, all with the same perimeter. We need to order them from greatest to least area. 2. **Formula and rules:** The peri

1. **Stating the problem:** Find the length of the hypotenuse $x$ of a right triangle where one leg is the radius of a circle with length 6, and the other leg outside the circle is

1. **Stating the problem:** We have a circle with radius 6, and a triangle formed by a radius, a segment outside the circle labeled 8, and the hypotenuse labeled $x$. We need to fi

1. **State the problem:** We have a large triangle composed of smaller triangles with given angles 40°, 30°, and 50°, and we need to find the unknown angle marked with a question m

1. **State the problem:** We need to find the perimeter of a rectangular rug with dimensions 6.25 feet by 8.5 feet. 2. **Formula for perimeter of a rectangle:**

1. **State the problem:** Calculate the volume of a trapezoidal prism with the following dimensions:

1. **State the problem:** We need to find the image of triangle \(\Delta TUV\) after reflecting it over the y-axis. 2. **Recall the reflection rule:** Reflecting a point \((x, y)\)

1. **Problem statement:** Given that FH bisects \(\angle EFG\), and the segments \(EF = 9x + 9\) and \(FG = 12x - 3\), find the measure of \(\angle EFH\). 2. **Understanding the pr

1. **State the problem:** We need to find the value of $n$ in a triangle with angles $(n + 17)^\circ$, $31^\circ$, and $75^\circ$. 2. **Recall the triangle angle sum rule:** The su

1. The problem asks to find the image of triangle UVW after reflecting it over the x-axis. 2. Reflection over the x-axis changes the y-coordinate of each point to its opposite, whi