📐 geometry

1. **Stating the problem:** We have a trapezoid ABCD with parallel sides AD and BC. Given are side AD = 5 cm, side AB = 12 cm, and the height (perpendicular distance from C to AB)

1. **State the problem:** Find the area of the kite with diagonals of lengths 1 and 2. 2. **Formula for the area of a kite:** The area $A$ of a kite is given by

1. The problem is to find the volume of a rectangular prism (in this case, a cube) with edge lengths of 5.1 inches each. 2. The formula for the volume $V$ of a rectangular prism is

1. **State the problem:** We are given a rectangular prism with length $9$ inches, width $5$ inches, and an unknown height. We need to find the height given the volume or find the

1. **Problem statement:** Given points A, B, C, A', B', C' on concurrent lines 𝓛, 𝓜, 𝓝 meeting at O, with AB \parallel A'B' and BC \parallel B'C', prove using Thales theorem that $

1. **Problem statement:** Given an isosceles triangle $\triangle ABC$ with $|AB| = |AC|$, and $M$ as the midpoint of $BC$, prove that the median $AM$ bisects the angle $\angle A$ a

1. **State the problem:** We have a semicircle with diameter $BC = 16$ cm and a triangle $ABC$ inside it. The angle at $A$ is $0.68$ radians. We need to find the area of the shaded

1. **Problem Statement:** Deduce that the diagonals of a rhombus meet at right angles. 2. **Definition and Properties:** A rhombus is a parallelogram with all sides equal in length

1. The problem is to show the image of a labeled parallelogram. 2. Since this is a request for an image and not a mathematical problem, I cannot provide a mathematical solution or

1. **Problem Statement:** Given a parallelogram with its two diagonals intersecting, find the pairs of congruent triangles using the parallelogram side theorem and ASA (Angle-Side-

1. **Problem statement:** Calculate the area of the shaded border region around a smaller rectangle inside a larger rectangle.

1. **Problem statement:** Show by induction that the angle sum of a convex $n$-gon is $$(n-2)\pi$$ for integer $n \geq 3$.

1. **Problem Statement:** Find the area of the shaded border around the inner rectangle.

1. **Problem 1: Decide if triangles ABC and DEF are similar.** Given side lengths:

1. **State the problem:** Among the proposed answers, identify the correct one for the first question: "The complement angle of 40° is:" 2. **Recall the definition:** The complemen

1. **State the problem:** We need to translate triangle ABC using the coordinate rule $(x,y) \to (x - 2, y + 4)$. This means each point of the triangle will be shifted 2 units left

1. The user asks how to find the midpoint ("milieu") of a segment. 2. The midpoint formula for a segment with endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$ is:

1. **Énoncé du problème :** On considère un triangle isocèle $ABC$ avec sommet principal $A$ tel que l'angle orienté entre $AB$ et $AC$ est $\frac{2\pi}{3}$ modulo $2\pi$. On note

1. The problem asks to draw the following angles in degrees: 34°, 69°, 93°, 147°, 198°, 255°, 283°, 316°, 331°, and 359°. 2. Angles are measured from the positive x-axis in a count

1. **Stating the problem:** We have a composite figure with parallelogram PQRS and rhombus RSTU. Given \(\angle QPS = 66^\circ\) and \(\angle RTU = 37^\circ\), we need to find \(\a

1. Let's start by stating the problem clearly: You want to solve a geometry question. 2. Geometry problems often involve formulas related to shapes, angles, lengths, areas, or volu