📐 geometry

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

1. **Problem 8: Find the volume of a right circular cylinder with diameter 8 cm and height 18 cm.** 2. The formula for the volume of a cylinder is $$V = \pi r^2 h$$ where $r$ is th

1. **Problem 1: Find the area of a trapezoid** with height $7.5$ ft and bases $7.5$ ft and $15$ ft. 2. The formula for the area of a trapezoid is:

1. **Problem statement:** We need to find the total surface area of a trapezoidal prism box including the flaps. The flaps area is given as 84 cm². 2. **Given dimensions:**

1. **Problem statement:** We have triangle ABC with point D on side AC such that segment BD bisects angle ABC. Given AB = 19, AD = 14, DC = 17, and BC = x, we need to find the valu

1. **State the problem:** A Ferris wheel has a diameter of 140 feet and 40 cars placed evenly around it. We need to find the distance between adjacent cars. 2. **Formula used:** Th

1. **Problem statement:** Given triangle ABC with segment BD bisecting angle ABC, sides AB = 18, BC = 19, AD = x, and DC = 11. We need to find the value of $x$. 2. **Formula used:*

1. **State the problem:** We need to find the exact surface area of a cylinder given its net.

1. **State the problem:** We are given a parallelogram with sides and angles labeled, and we need to find the values of $x$, $m\angle ADB$, and $m\angle A$. 2. **Use properties of