📐 geometry

1. **State the problem:** We have an isosceles triangle LMN with LM = LN. Lines AMB and CLN are parallel.

1. The problem asks to find the number of symmetry lines of a figure that is a circle divided into eight triangular sectors by radial lines. 2. A circle itself has infinite lines o

1. The problem asks to determine the shape of the cross-section formed by a horizontal plane intersecting the left and right faces of a cube. 2. A cube has six square faces, all ed

1. **Stating the problem:** We need to find the perimeter of the shaded region, which consists of an arc length plus three other segments labeled (1), (2), and (3).

1. **Problem statement:** Given a circle with center O and radius 8 m, points P, Q, and R lie on the circumference. OPQ is a straight line, \(\angle QOR = 36.9^\circ\), and OR is p

1. **Problem statement:** We need to find the length of segment $AD$ in a triangular pyramid with given angles and side lengths. 2. **Given data:**

1. **State the problem:** We are given pairs of adjacent angles on a straight line. Adjacent angles on a straight line are supplementary, meaning their sum is 180°. 2. **Formula us

1. The problem asks to visualize the 3D shape formed by two concentric squares positioned vertically with lines connecting them, enclosed in a larger rectangle, and considering the

1. The problem asks to identify the 3D shape represented by the nested squares and labeled points in the diagram. 2. The diagram shows two nested squares, one above the other, conn

1. The problem asks to visualize a 3D shape based on a description of two large squares stacked vertically, each containing a smaller square inside, connected by four parallel vert

1. The problem is to find the area, but the shape or figure is not specified. 2. To find the area, we need to know the type of figure (e.g., rectangle, triangle, circle) and its di

1. **Stating the problem:** We have a parallelogram ABCD with sides AB = 21 cm, BC = 25 cm, and angle BAD = 57°.

1. The problem is to understand and apply formulas in analytic geometry. 2. Analytic geometry uses coordinates and algebra to study geometric problems.

1. **State the problem:** We have a circle divided into five sectors with angles 31°, $f$, 73°, $g$, and one unknown angle. We need to find the size of angle $f$ and then use it to

1. The problem is to find which angles are complementary. 2. Complementary angles are two angles whose measures add up to 90 degrees.

1. The problem involves identifying relationships between pairs of angles formed by intersecting lines at point F, where a right angle is indicated. 2. Important rules:

1. The problem asks to determine which pairs of angles are adjacent among the given pairs: $\angle 5$ and $\angle 10$, $\angle 2$ and $\angle 9$, $\angle 2$ and $\angle 10$, $\angl

1. **State the problem:** We have a right triangle with hypotenuse 30m, base 14m, and we need to find the angle $x$ opposite the base. 2. **Formula used:** In a right triangle, the

1. **State the problem:** We have a right-angled triangle with two sides given: one side is 7 cm and the other is 5 cm. We need to find the length of the hypotenuse. 2. **Formula u

1. **Problem:** Find an equation of the sphere with center $(-1,4,5)$ that just touches the a. xy-plane,

1. **Stating the problem:** We are given the formula for the area of a rectangle or parallelogram, which is $A = b \times h$, where $A$ is the area, $b$ is the base, and $h$ is the