📐 geometry

1. **Problem Statement:** Quadrilateral ABCD is dilated to form quadrilateral EFGH. We are given side lengths of ABCD as 8 (CB) and 10 (BA), and corresponding side lengths of EFGH

1. **Problem Statement:** Given that triangles $\triangle ABC$ and $\triangle MNP$ are similar, determine which of the following statements is true: I. $\frac{AC}{BC} = \frac{MP}{N

1. **פתרון תרגיל 1:** א. נתונות משוואות הצלעות AB ו-CD בטרפז:

1. **Problem Statement:** Given quadrilateral ABCD with point O inside it, and points W, X, Y, Z as midpoints of segments AO, BO, CO, and DO respectively, prove that quadrilateral

1. **Stating the problem:** We need to find the size of the angle $\alpha$ in the given geometric configuration involving a rectangle, two circles (one smaller with radius $r$ and

1. **Stating the problem:** We have two parallel lines "a" and "b" cut by a transversal. The angle adjacent to the transversal on line "a" is $3x + 30^\circ$ and the corresponding

1. **Stating the problem:** We have a mobile login screen layout composed of geometric shapes with given vertices:

1. **State the problem:** We have a parallelogram KLMN with angles at vertices N and L given by $7x - 30^\circ$ and $5x + 18^\circ$ respectively. We need to find the value of $x$ a

1. **Problem Statement:** We have a parallelogram KLMN with angles at vertices L and N given by $5x + 18^\circ$ and $7x - 30^\circ$ respectively.

1. **Problem Statement:** Find the volume and total surface area (TSA) of a sphere with a radius of 4 cm. 2. **Formulas:**

1. **Problem Statement:** Prove that the points (4, 3), (6, 4), (5, 6), and (3, 5) are the vertices of a square. 2. **Formula and Rules:** To prove a quadrilateral is a square, we

1. **Problem statement:** Given triangle $AB\Gamma$ with $AB < A\Gamma$, $M$ is the midpoint of $B\Gamma$. A perpendicular from $M$ to $B\Gamma$ meets the extension of the bisector

1. **State the problem:** We need to find the total surface area of a frustum formed by removing a smaller cone from a similar larger cone. The large cone has slant height $l=42$ m

1. **Problem statement:** We are given a square with a diagonal length of 8 cm and need to find the side length of the square in simplest form. 2. **Formula used:** For a square wi

1. The problem asks for the coordinates of point R plotted on a Cartesian plane. 2. Coordinates are given as an ordered pair $(x, y)$ where $x$ is the horizontal position and $y$ i

1. **Problem Statement:** We have a right triangle with legs of lengths 3.6 meters and 2.7 meters. We want to find the length of the hypotenuse (the tube leaning against the wall).

1. **State the problem:** We have a triangle with three angles: 30°, 2x, and x. We need to write an equation for the sum of these angles and find the value of $x$. 2. **Formula use

1. **State the problem:** Find the volume of a sphere with radius $r=9$ units. 2. **Formula:** The volume $V$ of a sphere is given by the formula:

1. Let's state the problem: We want to understand the properties of a coin modeled as a cylinder. 2. A cylinder is a 3D shape with two parallel circular bases connected by a curved

1. The problem is to find the midpoint of a line segment given two points and then find the point above this midpoint. 2. The midpoint formula for two points $A(x_1,y_1)$ and $B(x_

1. The problem asks to find the height of the photo taken, but no numerical data or measurements are provided in the description. 2. To find the height of a photo or an object in a