📐 geometry

1. **Problem statement:** We have an acute triangle with sides $x$, $2x$, and $15$ cm, where $15$ cm is the longest side. We need to find the smallest whole-number value of $x$ suc

1. **Problem statement:** We have an acute triangle with two known sides measuring 5 inches and 8 inches. We want to find the greatest possible whole-number length of the unknown l

1. The problem asks to name three points in the given diagram of a parallelogram. 2. From the description, the points given are P, T, U, S, R, Q, and O.

1. The problem asks to name three points from the given diagram. 2. From the description, points are labeled as O, M, K, L, P, N, J, and others.

1. **State the problem:** We are given an isosceles triangle with two equal sides and two angles: one angle is $ (8x - 23)^\circ $ and the opposite angle is $ 34^\circ $. We need t

1. **State the problem:** We need to find the distance between two points $A(1, 9)$ and $B(-4, -3)$ in the coordinate plane. 2. **Formula used:** The distance $d$ between two point

1. **State the problem:** We need to find the distance between two points $A(3, 8)$ and $B(-1, 1)$ in the coordinate plane. 2. **Formula used:** The distance $d$ between two points

1. **State the problem:** We have a pre-image with points B(8,4), U(6,10), N(5,-2) and an image with points B'(2,1), U'(1.5,2.5), N'(1.25,-0.5). We need to find the transformation

1. The problem states that we have two intersecting lines forming vertical angles. 2. Vertical angles are always equal.

1. **State the problem:** We have two similar quadrilaterals WXYZ and LMNP. The angles of WXYZ are given as $\angle W = 112^\circ$, $\angle X = 74^\circ$, $\angle Z = 72^\circ$, an

1. **State the problem:** We are given two triangles with sides labeled and asked which proportion could NOT be used to solve for $x$ given the sides: $$\frac{x}{5} = \frac{35}{9}$

1. The problem asks for the ratio of the area of the smaller square to the area of the larger square given their side lengths. 2. Recall the formula for the area of a square: $$\te

1. The problem asks for the ratio of the area of the larger circle to the area of the smaller circle. 2. Recall the formula for the area of a circle: $$A = \pi r^2$$ where $r$ is t

1. The problem asks which angle in the translated figure corresponds to angle $RST$ in the original figure after a translation 9 units to the right. 2. Translation moves every poin

1. **Problem statement:** Find the surface area of a triangular prism with triangle side lengths 9 in., 12 in., and 15 in., and height (depth) 12 in. 2. **Formula for surface area

1. The problem asks if Kirby's expression for the surface area of a rectangular prism is correct. 2. The formula Kirby gives is:

1. **Problem Statement:** Determine which conclusions must be true for a quadrilateral that has a line of symmetry.

1. **Problem Statement:** We have two congruent triangles, Figure 1 with vertices C, B, A and Figure 2 with vertices F, E, D. We need to determine which sequences of transformation

1. The problem asks to find the measure of each interior angle of the shelf and the sum of the interior angles. 2. The formula for the sum of interior angles of a polygon with $n$

1. **State the problem:** We need to find the area of a piece of land shaped as a combination of a trapezoid and a parallelogram. 2. **Identify the dimensions:**

1. **State the problem:** Find the volume of a right circular cylinder with diameter 8 cm and height 18 cm. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h