📐 geometry

1. Stating the problem for Day 4: Given quadrilateral ABEDC with triangles ABE and DEC, determine the nature of these triangles, show that angle AÊB = 70°, and deduce the measure o

1. **Problem statement:** Calculate the volume of the part of the cone that is not in contact with water when a conical solid of radius 14 cm is fitted into a cylindrical tin of ra

1. **Problem Statement:** ABCD is a rhombus where the altitude from vertex D to side AB bisects AB. We need to find the angles of the rhombus. 2. **Understanding the problem:** A r

1. **Problem Statement:** Given triangle ABC, right-angled at B, and D is the midpoint of AC. We need to prove that $DA = DB = DC$. 2. **Understanding the problem:** Since $D$ is t

1. **Problem Statement:** Calculate the total volume of units 1 to 15, each with a height of 3 meters. 2. **Given Data:** Each unit has a floor area defined by the floor plan. The

1. **Stating the problem:** We need to find the angle $x$ in a quadrilateral with given angles $100^\circ$ and $126^\circ$ and two pairs of equal sides. 2. **Understanding the prop

1. **Đề bài:** Cho tam giác vuông $\triangle ABC$ vuông tại $A$. Qua điểm $C$ kẻ đường thẳng $d$ vuông góc với $AC$. Trên $d$ lấy điểm $E$ sao cho $CE=AB$ và $E$, $B$ thuộc hai nửa

1. ସମସ୍ୟା କହାଯାଇଛି: ଏକ ବୃତ୍ତର ବ୍ୟାସାର୍ଦ୍ଧ $15$ ସେମି ଓ ଏକ ଜ୍ୟାର ଦୈର୍ଘ୍ୟ $24$ ସେମି ଦିଆଯାଇଛି। 2. ବୃତ୍ତର ବ୍ୟାସାର୍ଦ୍ଧ ହେଉଛି ବ୍ୟାସ $d=15$ ସେମି, ତେଣୁ ବୃତ୍ତର ତ୍ରିଜ୍ୟା $r=\frac{d}{2}=\frac{

1. **Problem statement:** We have a semicircle PQRS with center O and radius $r$. The semicircle is divided into three arcs of equal length by points P, Q, R, and S. We need to fin

1. **Problem:** Find the radius of a cylinder with height $27$ mm and volume $4300$ mm$^3$. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is

1. **Nyatakan masalah:** Diberi sektor bulatan OABC dengan OA = AC = 6 cm dan DC adalah lengkok sukuan bulatan. OD adalah pembahagi dua sama serenjang perentas AC.

1. **Stating the problem:** We have points A, B, C, and D on a school land plot with given distances and angles. We need to find the required gravitational force (or weight) and re

1. The problem asks to find the value of angle R in a regular polygon with five sides (a regular pentagon). 2. In a regular polygon, all interior angles are equal. The formula to f

1. مسئله: دو مثلث با اضلاع 5, 12, 13 و 5.58, 18, 13.2 داده شده‌اند که متشابه هستند. باید مساحت مثلث بزرگ‌تر را پیدا کنیم. 2. ابتدا بررسی می‌کنیم که آیا این دو مثلث متشابه هستند یا

1. **State the problem:** We need to find the area of a composite shape made of two polygons: a quadrilateral on the left and a triangle on the right. 2. **Identify the shapes and

1. **Problem statement:** Determine the unknown side lengths and angles in the similar triangles given. 2. **Given:** Triangles with sides and angles: one triangle with side 22 m o

1. **Problem statement:** We have trapezoid ABCD with an angle bisector \(\overline{AC}\) dividing it into two similar triangles \(\triangle ABC\) and \(\triangle ACD\). Given legs

1. **Problem Statement:** Design orthogonal, isometric, and perspective drawings of a greenhouse with given dimensions and scales. 2. **Given Data:**

1) a) **Show that $\angle FEM = \angle MAB$.** 1. We are given that $G$ is the symmetric of $E$ with respect to $F$, and $C$ is the symmetric of $A$ with respect to $B$.

1. **Problem statement:** Given an isosceles triangle $\triangle ABC$ with $AB = AC$. Points $D$ and $E$ are taken on the rays opposite to $BC$ and $CB$ respectively such that $BD

1. **Problem statement:** In triangle PQR, angles R and Q are bisected by lines RU and QS respectively. Given that angle P = 50° and angle TRS = 32°, find the measure of angle QTU.