📐 geometry

1. Problem: Find $x$ in a circle where angles 110°, 25°, and $x$ are related. 2. Formula: The sum of angles around a point on a circle is 360°.

1. **Problem statement:** Iris wants to find the total length of wood needed to construct triangle \(\triangle DFG\), which is similar to \(\triangle ABC\). Given sides of \(\trian

1. The problem is to find the volume of the square pyramid at the START position, which has a base edge of 6 inches and height 6 inches. 2. The formula for the volume of a square p

1. **Problem Statement:** Given multiple triangles with labeled sides and vertices, find the unknown side lengths using similarity properties. 2. **Similarity Rule:** Triangles are

1. Problemi: Gjej sa centimetra ka kaluar akrepi i madh i ores per 45 minuta nese gjatesia e tij eshte 14 cm. 2. Formula qe perdorim eshte per gjatesine e harkut te nje rrethi: $$L

1. **Stating the problem:** We have a large equilateral triangle ABC with sides AB = 7 cm, AC = 5 cm, and BC = x cm. Smaller equilateral triangles are drawn along the sides from co

1. **State the problem:** LaTanya wants to find the midpoint between points A and B to center a picture along the back wall.

1. Stwierdzenie problemu: Mamy trójkąt $\triangle ABC$ z bokami $|AB|=12$, $|AC|=10$ oraz kątem $|\angle ACB|=60^\circ$. Należy wyznaczyć długość boku $|BC|$. 2. Wzór: Skorzystamy

1. Stated problem: Given triangle $\triangle ABC$ with sides $|AB|=6$, $|BC|=8$, and angle $\angle ABC=120^\circ$, find the length of side $|AC|$. 2. Formula used: To find the leng

1. **Problem:** Given triangle $\triangle ABC$ with $|AB|=6$, $|BC|=8$, and $\angle A + \angle BC = 120^\circ$, find the length of side $|AC|$. 2. **Formula and rules:** We use the

1. **Problem Statement:** Find the value of $x$ in a right triangle where one angle is $45^\circ$, the base is 15, and the hypotenuse is $x$.

1. **State the problem:** We have a triangle with sides of lengths 8, 10, and 12 units. We want to find the approximate measure of angle $G$. 2. **Identify the sides relative to an

1. **Problem statement:** Find the height $x$ of an equilateral triangle with side length 14 inches. 2. **Formula and rules:** In an equilateral triangle, all sides are equal and a

1. **State the problem:** We have a right square pyramid with an altitude (height) of 10 units and a base side length of 6 units. We need to find the distance from the apex (top) t

1. **State the problem:** We need to find the image of rhombus BCDE after a 90° anticlockwise rotation around the origin. 2. **Recall the rotation formula:** For a point $(x,y)$, a

1. **State the problem:** We want to find the perimeter of a quadrilateral formed by two scalene triangles. We only know two sides of one triangle and one side of the other. 2. **U

1. **Problem 106: Find the length of X in the right triangle**. Given a right triangle with legs 4 and 4, and hypotenuse 7, find the length of segment X.

1. **Problem statement:** The areas of a circle and a rectangle are equal, and the area of the shaded region (the overlapping part) is 10 cm². We need to find the area of the recta

1. **הבעיה:** במשולש ABC חסום במעגל, נקודה N על הקשת AB היא מרכז מעגל העובר דרך A ו-B וחותך את המיתר AC בנקודה D. המיתר NC חותך את המעגל שמרכזו N בנקודה E ואת המיתר AB בנקודה F. נד

1. **Problem Statement:** Enlarge each shape by the given scale factor using the specified centre of enlargement.

1. The problem is to enlarge shapes by given scale factors from specified centres of enlargement. 2. The formula for enlargement of a point $(x,y)$ from centre $(x_c,y_c)$ with sca