📐 geometry

1. **State the problem:** We have a scale of 1 : 500, meaning 1 unit on the drawing represents 500 units in reality. 2. **Given:** Actual area = 125,000 m². We need to find the are

1. **State the problem:** We have a scale of 1 : 500, meaning 1 unit on the drawing represents 500 units in reality. 2. **Given:** Actual area = 125,000 m². We want to find the are

1. **Problem Statement:** Construct triangle XYZ with sides |YZ| = 6 cm, |ZX| = 6 cm, and |ZY| = 9 cm, and angle YZX = 60°.

1. **State the problem:** We need to find the size of angle $x$ in a right triangle with sides 9.7 cm (vertical) and 5.1 cm (horizontal). 2. **Formula used:** To find an angle in a

1. **State the problem:** We have a scale drawing of a classroom with dimensions 9.6 cm by 7.2 cm, drawn at a scale of 1 : 75. We need to find the actual dimensions of the classroo

1. **State the problem:** We need to find the arc measure of the minor arc \(\stackrel{\large{\frown}}{BC}\) in degrees on a circle centered at point P with points A, B, C, and D o

1. **State the problem:** We have a scale of 1 : 1000, meaning 1 unit on the drawing represents 1000 units in reality. 2. **Given:** Actual distance between two villages is 2.4 km.

1. The problem asks to find the image that is different as a result of reflection among the given options. 2. Reflection means flipping a figure over a line (mirror line) so that t

1. Stating the problem: We need to find the volume and surface area of two vertical cylinders. 2. Formula for a cylinder:

1. **State the problem:** We have a rectangular garden measuring 30 m by 18 m, drawn to a scale of 1 : 300. We need to find the dimensions of the drawing in cm and then calculate t

1. The problem asks: "An inscribed angle is an angle with its vertex on the _____________ of the circle." The correct answer is "edge" or "circumference" because an inscribed angle

1. **Problem 1:** Given right angles \(\angle ABD = \angle CDB = \angle PQB = 90^\circ\), and lengths \(AB = x\), \(CD = y\), \(PQ = z\), prove that \(\frac{1}{x} + \frac{1}{y} = \

1. **Problem Statement:** In the figure, \(\angle ABD = \angle CDB = \angle PQB = 90^\circ\). Given \(AB = x\), \(CD = y\), and \(PQ = 2\), prove that \(\frac{1}{x} + \frac{1}{y} =

1. The problem is to verify the area of a rectangle given its side lengths and the stated area. 2. The formula for the area of a rectangle is:

1. **State the problem:** We need to find the size of the angle marked with the letter $k$ in the triangle. 2. **Identify given angles:** The triangle has an angle of $20^\circ$ at

1. The problem asks to find the area of a sector of a circle with radius $10$ cm and central angle $66^\circ$. 2. The formula for the area of a sector is:

1. **Stating the problem:** We are given a circle with points E, S, T and angles related to these points. We need to find the measures of angles and segments: $m\angle E$, $mSET$,

1. **Problem statement:** Identify the parts of the quadrilateral illustrated by the given points, segments, and angles. 2. **Understanding the quadrilateral:** The quadrilateral i

1. The problem asks to name the angle relationship between \(\angle 2\) and \(\angle 8\).\n\n2. Since lines \(p\) and \(q\) are parallel and \(s\) is a transversal, \(\angle 2\) an

1. **Problem statement:** Given two parallel lines \(\overline{NO} \parallel \overline{PQ}\) and points as described, find the measure of angle \(m \angle QSR\). 2. **Identify give

1. **Problem statement:** Given triangle ABC with XZ parallel to BC, AZ = 3 cm, ZC = 2 cm, BM = 3 cm, and MC = 5 cm, find the length of XY. 2. **Key concept:** When a line segment