📐 geometry

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

1. The problem is to find the angle given the final answer is 40°. 2. Since the final answer is already provided as 40°, no further calculations are needed.

1. **Problem statement:** We have a parallelogram PQRS and a rhombus RSTU with S on OT. Given \(\angle QPS = 66^\circ\) and \(\angle RTU = 37^\circ\), find \(\angle PSO\). 2. **Key

1. **Problem statement:** We are given a figure with parallelogram PQRS and rhombus RSTU sharing side RS. Point S lies on OT. Given angles are \(\angle QPS = 66^\circ\) and \(\angl

1. **State the problem:** We have a square-based pyramid with a slant edge of 13 cm and a base length of 10 cm. We need to find the slant height of the pyramid. 2. **Understand the

1. Let's start by stating the problem: We need to understand the basics of circles in math. 2. The general equation of a circle with center at $(h,k)$ and radius $r$ is given by:

1. **State the problem:** We have two circles: one centered at point A with radius equal to the length of segment AB, and another centered at point C with the same radius AB. These

1. **Problem Statement:** Prove that each diagonal of a rectangle divides it into two congruent triangles. 2. **Recall the properties of a rectangle:**

1. **State the problem:** Find the area of a polygon with right angles and given side lengths: bottom 13 in, two vertical sides 6 in each, two vertical segments 4 in each at the to

1. **State the problem:** Find the area of a polygon with sides meeting at right angles and given side lengths. 2. **Approach:** Since the polygon is rectilinear (all angles are ri

1. **State the problem:** Find the area of an irregular polygon composed of three rectangular segments with right angles. 2. **Analyze the figure:** The base length is 13 inches, h

1. **State the problem:** Find the area of a parallelogram with base $14$ yd and height $14$ yd. 2. **Formula:** The area $A$ of a parallelogram is given by:

1. The problem states that triangles $\triangle ABC$ and $\triangle CBE$ are congruent, i.e., $\triangle ABC \cong \triangle CBE$. 2. This means all corresponding sides and angles