📐 geometry

1. **Problem statement:** We have three lines AB, BC, and CD with given lengths and directions. A reversed curve connects these lines, and we need to find the length of the common

1. The problem asks to measure one interior angle in each polygon. 2. The sum of interior angles in a polygon with $n$ sides is given by the formula:

1. **Problem:** Measure the marked interior angle in each polygon by extending the arms of the angle and using a protractor or angle measurement method. 2. **Formula and rules:** T

1. **State the problem:** We need to find the value of $x$ for a triangle where the area is $\sqrt{5} \times 3$, the angle between the base and the side is $60^\circ$, the base len

1. Problem: Find the measure of angle $\angle MCB$ given arc $AM = 40^\circ$ and arc $BK = 60^\circ$. 2. Formula: The angle formed by two chords intersecting on the circumference i

1. Énonçons le problème : Mme veut tracer le périmètre d'une œuvre d'art composée de plusieurs carrés dont les aires sont données : 100 cm², 16 cm², 289 cm², et 64 cm². 2. Rappelon

1. **State the problem:** We need to prove that triangles $\triangle TRS$ and $\triangle QRP$ are congruent given that $SR \cong PR$, $TQ$ is perpendicular to $TS$, and $TQ$ is per

1. **Problem statement:** An aircraft moves from station P(25°N, 15°E) to station Q(25°N, 23°W) along the parallel of latitude, then from Q to R(35°S, 23°W) along the meridian. We

1. **Problem Statement:** Classify the segments \(\overline{KM}\), \(\overline{CD}\), and \(\overline{PS}\) in their respective triangles based on the given figure and markings. 2.

1. **Problem statement:** We have triangle $\triangle TUV$ with medians $\overline{TX}$, $\overline{UY}$, and $\overline{VW}$ intersecting at centroid $Z$. Given $UY=33$, $TZ=8$, a

1. **State the problem:** We have a small square with side length 20 mm. 13 copies of this square are arranged to form a larger rectangle. We need to find the area of the larger re

1. **Problem Statement:** We have a 5 by 5 diamond grid composed of 25 smaller squares. A path starts at the bottom vertex and moves upward to the top vertex, moving either northea

1. **Problem Statement:** Find the perimeter and area of the rectangle with vertices A(-1, 1), B(3, 1), C(3, -4), and D(-1, -4). 2. **Formula for Perimeter of a Rectangle:**

1. **Problem statement:** Determine the length of side $c$ in each triangle $\triangle ABC$ given the sides and angle.

1. The problem asks to describe the locus of points inside rectangle PQRS that are equidistant from sides PQ and RS. 2. Recall that the locus of points equidistant from two paralle

1. **State the problem:** We have two points A and B, 5 cm apart, and we want to construct the locus of points equidistant from A and B. 2. **Key concept:** The locus of points equ

1. **Problem Statement:** We need to find the locus of points equidistant from the line segments PR and QR in triangle PQR. 2. **Key Concept:** The locus of points equidistant from

1. The problem asks to identify the locus of points that are 4 cm away from a fixed point P. 2. The locus of points at a fixed distance from a point is a circle.

1. **State the problem:** We have a triangle with sides 7.1 cm and 8.5 cm, and an angle of 74° between them. We need to find the length of side $b$ opposite the 74° angle. 2. **For

1. **State the problem:** Given triangle $\triangle QRS$ with circumcenter $W$, and segments $QR=32$, $RU=19$, $QV=24$, and $VS=21$, find the lengths of $RS$, $TQ$, $WS$, $QV$, and

1. **Problem statement:** Given a circle with points S, T, and R, and the angle \(\angle STR = 42^\circ\), find the unknown angle at point T between points S and R. 2. **Understand