📐 geometry

1. **Problem statement:** We have two triangles, A and B, on a coordinate grid. Triangle A is translated to form triangle B. We need to find the values of $d$, $e$, and $f$ which a

1. **State the problem:** We start at point A (0,0). Travel 7 km on a bearing of 135° to point B. Then from B, travel 12 km on a bearing of 250° to point C. We need to find the dis

1. **State the problem:** We are given a kite ABCD with sides labeled as expressions involving variables $v$ and $w$: - $AB = 10v - 13$

1. **State the problem:** We need to find the area of a trapezium with bases $a=8$ cm, $b=9$ cm, and height $h=6$ cm. 2. **Formula:** The area $A$ of a trapezium is given by the fo

1. **Problem statement:** Find the values of the angles marked with letters in the given diagrams. 2. **Focus on part (b):** Given $b=80^\circ$ and $a=\frac{3}{2}c$, find angles $a

1. **Problem statement:** We need to find the length of side $AB$ in the triangular prism. Given are angle $\angle F = 24^\circ$, side $FE = 6$ cm, and slant height $EC = 13$ cm. 2

1. **Problem Statement:** Given triangle $ABC$ with midpoints $D$, $E$, and $F$ of sides $BC$, $CA$, and $AB$ respectively, prove that the medial triangle $DEF$ is similar to $ABC$

1. Let's consider the example of a rotation around the origin by an angle $\theta = \frac{\pi}{4}$ (45 degrees) counter-clockwise. 2. The rotation transformation is given by the fo

1. The problem is to plot the locations of various landmarks on a Cartesian coordinate plane based on their relative positions to the Church at the origin (0,0). 2. The Church is a

1. Let's start by stating the problem: We want to understand what similar triangles are and how to identify them. 2. Definition: Two triangles are similar if their corresponding an

1. **Problem statement:** We have a right-angled triangle XYZ with sides XY = 8 cm and YZ = 12 cm. Inside it, a rectangle ABCY is drawn such that B lies on XZ and AY = x cm.

1. **Problem statement:** We have a right-angled triangle XYZ with legs XY = 8 cm and YZ = 12 cm. Inside it, a rectangle ABCY is drawn such that AY = x cm and B lies on the hypoten

1. **Problem Statement:** Determine if the triangle with vertices at points $(2,3)$, $(4,9)$, and $(-2,7)$ is isosceles. 2. **Formula Used:** To check if a triangle is isosceles, w

1. **Problem Statement:** We are given a polygon with four sides and three angles labeled as $2x$, $3x$, and an exterior angle $4x$. We need to find the value of $x$. 2. **Understa

1. **State the problem:** We have a right triangle with angle B = 63° and angle A = 27° (since the sum of angles in a triangle is 180° and the right angle at C is 90°). 2. **Identi

1. **State the problem:** We are given a triangle XYZ with angles labeled as $x + 2$, $2x + 23$, and $3x + 5$. We need to find the value of $x$. 2. **Recall the triangle angle sum

1. **State the problem:** We are given a triangle XYZ with angles labeled as follows: angle X = $x + 2$, angle Y = $2x + 23$, and angle Z = $3x + 5$. We need to find the value of $

1. **State the problem:** We need to find the measure of angle $\angle BHD$ given two expressions for angles formed by a transversal crossing two parallel lines. 2. **Given:**

1. **Stating the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((89 - 6x)^\circ\) and \((3x + 62)^\circ\). We need to

1. **State the problem:** We need to find the measure of angle $\angle QWU$ given two expressions for angles formed by parallel lines and a transversal. 2. **Identify the angles an

1. **State the problem:** We have two parallel lines cut by a transversal, creating angles at points M and N. 2. **Identify the angles:** The angle at M is $(3x + 10)^\circ$ and th