📐 geometry

1. **State the problem:** We need to find the length of side $g$ in triangle $GEF$ where angles and some sides are given. 2. **Given:**

1. **State the problem:** We have a dilation of a black polygon to a blue polygon with center of dilation at point $P$. We need to determine if the dilation is an enlargement or re

1. Problemet är att hitta arean som är 1700 cm². 2. Om vi antar att vi har en rektangel eller annan figur, måste vi veta dess dimensioner eller formel för att bekräfta detta.

1. Problemet är att beräkna arean av triangeln ABC där vi vet att det är en rätvinklig triangel med en katet (sida intill den räta vinkeln) på 40 cm och hypotenusan på 60 cm. 2. Fo

1. Problem (i): Prove that a point O equidistant from points A and B lies on the perpendicular bisector of segment AB. 2. Recall the definition: The perpendicular bisector of a seg

1. **State the problem:** We have a large cone with height $42$ mm and radius $6$ mm. It is split horizontally into a smaller similar cone at the top with height $14$ mm and radius

1. **State the problem:** We need to find the volume of the frustum of a rectangular-based pyramid. The frustum is formed by cutting a larger pyramid horizontally, leaving a smalle

1. Problem (i): Prove that a point O equidistant from points A and B lies on the perpendicular bisector of segment AB. 2. Recall the definition: The perpendicular bisector of a seg

1. **Stating the problem:** We need to find the difference between the total green shaded area and the total blue shaded area on a grid with a scale in centimeters. 2. **Understand

1. The problem involves understanding the relationship between the angles and sides of two parallelograms in a tiled pattern. 2. Key properties of parallelograms:

1. **Problem Statement:** We have a mechanical jack shaped as a parallelogram with all four arms of equal length (a rhombus). The crank is 5 inches above the ground, and we want to

1. **Problem Statement:** We have a mechanical jack shaped as a parallelogram with all four arms of equal length. The crank is 5 inches above the ground, and we want to find the he

1. **State the problem:** Given a parallelogram ABCD with AB \parallel DC and AD \parallel BC, prove that opposite angles are congruent: \(\angle A \cong \angle C\) and \(\angle B

1. **Problem Statement:** If a quadrilateral is a parallelogram, prove that its opposite sides are congruent and its diagonals bisect each other.

1. **State the problem:** We are given a parallelogram with sides labeled as follows: top side = $12 - c$, left side = $2b$, bottom side = $c - 2$, right side = $4b - 6$. We need t

1. **Stating the problem:** We have two adjacent parallelograms sharing a bottom angle, with the top left angle of the upper parallelogram given as $41^\circ$ and the top right ang

1. **Problem:** How many triangles can you identify in the given figure where a square is divided by its diagonals into four triangles, then further divided by a vertical line thro

1. **Problem statement:** We have a six-pointed star made up of 6 identical quadrilaterals. Each quadrilateral has angles marked $x$ and two angles marked $25^\circ$. We need to fi

1. **Stating the problem:** We have a horizontal line segment AB of length 8 cm.

1. **State the problem:** Calculate the volume of a shape made from a triangular prism with a rectangular hole through the middle. 2. **Identify the dimensions:**

1. The problem involves identifying congruent angles and setting up a proportion to show that two triangles are similar. 2. From the given labels, Angle C is congruent to Angle A b