📐 geometry

1. **State the problem:** Determine if quadrilateral C B A D is congruent to quadrilateral E F G H by using transformations. 2. **Recall the definition of congruence:** Two figures

1. **Stating the problem:** Calculate the volume of a rectangular parallelepiped with a base area of 540 dm², where one side of the base is $\frac{3}{5}$ of the other, and the late

1. The problem asks whether a right triangle with two congruent legs is always a 45-45-90 triangle. 2. A right triangle has one 90-degree angle.

1. **State the problem:** We have a right isosceles triangle with angles 45°, 45°, and 90°, and the hypotenuse length is 22. We need to find the length of each leg. 2. **Formula an

1. **State the problem:** We need to find the coordinates of the vertices of rectangle URTS after a 90° counterclockwise rotation around the origin. 2. **Formula for 90° counterclo

1. **State the problem:** We need to find the coordinates of the vertices of triangle RQS after a 180° counterclockwise rotation around the origin. 2. **Formula for rotation:** A 1

1. The problem asks to find the distance in Roblox studs between two players in a 3D game scene. 2. To find the distance between two points in 3D space, we use the distance formula

1. **State the problem:** We have a figure composed of a rectangle topped by a triangle. The rectangle has length 5 cm and width 3 cm. The triangle has side lengths 5 cm, 3 cm, and

1. **State the problem:** We need to find the perimeter of a trapezoid with a bottom base of 8 cm, a top base of 5 cm, and two sides each measuring 6 cm. 2. **Formula for perimeter

1. **State the problem:** We need to find the perimeter of a trapezoid with a bottom base of 11 cm, a top base of 7 cm, and two sides each measuring 8 cm. 2. **Recall the formula f

1. The problem is to find the measure of angle EAB modulo 360 degrees, which means finding the equivalent angle between 0 and 360 degrees. 2. The modulo operation for angles is giv

1. **State the problem:** We have a rectangle ABCD with diagonals AC and BD intersecting at point E. Given that $BD = 4x - 2$, $AC = 5x - 10$, and $m\angle EDA = 39^\circ$, find th

1. **Problem Statement:** Determine the surface area and volume of a rectangular prism with dimensions 7, 4, and 12. 2. **Formulas:**

1. **State the problem:** We have a right triangle with hypotenuse $25$ and one leg $21$. We need to find the length of the other leg $x$ using the Pythagorean theorem. 2. **Formul

1. **Stating the problem:** We are given a geometric figure with angles and arcs, and we need to find the value of angle $\alpha$. The figure includes a large semicircle with a tri

1. **State the problem:** Given two parallel lines $a \parallel b$ cut by a transversal, prove that $\angle 3 \cong \angle 6$. 2. **Recall the relevant theorem:** When a transversa

1. **Problem 1: Find the area of the shaded section inside the large circle with two smaller circles stacked vertically.** 2. The large circle contains two smaller circles stacked

1. **Énoncé du problème** : Trouver le point d'intersection B des droites $D_1$ et $D_3$. 2. **Données** :

1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal, and two angles: one is $(10x+1)^\circ$ below the top line $m$, and the other is $(5x+29)

1. **State the problem:** Given two parallel lines $m \parallel n$ cut by a transversal $t$, find the value of $x$ given the angles $(5x+23)^\circ$ and $(6x-4)^\circ$. 2. **Identif

1. The problem asks to find the image of figure ABCDEFGH after a dilation with scale factor 2. 2. Dilation with scale factor 2 means every point of the figure moves away from the c