📐 geometry

1. The problem asks to identify the figure based on the description and partial calculations provided. 2. From the given data, we see calculations involving areas of squares and ci

1. **State the problem:** We need to find the sum of the interior angles of a polygon. 2. **Formula:** The sum of the interior angles of a polygon with $n$ sides is given by:

1. **State the problem:** We need to find the measure of $$\angle x$$, which is $$\angle M O L$$, given that $$\angle M O N = 133^\circ$$ and lines $$L N$$ and $$M O$$ intersect at

1. **State the problem:** Construct parallelogram $ABCD$ with $AB=10$ cm, $AD=6.5$ cm, $\angle BAD=110^\circ$, and $\angle ABC=70^\circ$. Then measure diagonal $AC$ and construct l

1. **Nêu bài toán:** Cho tam giác $ABC$ vuông tại $A$, $BM$ là đường trung tuyến, $K$ là điểm trên tia đối tia $MB$ sao cho $MK = MB$. Chứng minh: a) $CK$ vuông góc $AC$

1. ප්‍රශ්නය: ABCDEF සන්කේතයේ O පාදය සහ a පසිය ඇති ත්‍රිකෝණයක් දී, AB=2P, BC=4P, DE=5P, FA=6P ලෙස දී ඇත. CF රේඛාව O සිට දුර $$\frac{17a}{2}$$ ලෙස දී ඇත. CD සහ EF දිගවල අන්තර් පරිවර්

1. **ප්‍රශ්නය**: (i) සිරස් බිත්තියකට හේත්තු කර ඇති 410 cm දිග ඉනිමඟක ඉහල කෙළවර බිත්තිය පමණ 400cm ක ඉහලින් පිහිදී. බිත්තිය හාමුල සිට ඉනිමේ පහළට ඇති දුර සොයන්න. (ii) කුපර් නම ගෝලයකින

1. **Problem:** Solve for $x$ in the diagram with two parallel lines cut by a transversal, angles given are $26^\circ$, $64^\circ$, and $x^\circ$.\n\n2. **Formula and rules:**\n- T

1. **Problem Statement:** In quadrilateral MNPS, a line through point N cuts SP at Q. Given:

1. **State the problem:** We need to find the length of side $PQ$ in triangle $PRQ$ where $R$ is the top vertex, the altitude from $R$ to $PQ$ is $7.4$ cm, and the angles at $P$ an

1. **State the problem:** We need to find the measure of $\angle BEC$ in the given figure where $EC$ is perpendicular to $BA$, $\angle C = 39^\circ$, and the sides $BE = 4.6$ m and

1. **Problem:** Find the value of an angle $x$ such that $100$ less than two times its supplement equals thrice its complement. 2. **Recall definitions:**

1. **Problem:** Find the value of an angle $x$ such that $100$ degrees less than two times its supplement equals thrice its complement. 2. **Step 1: Define the supplement and compl

1. **State the problem:** We have a scale drawing of a shed with dimensions $15.2\text{ cm}$ by $12.5\text{ cm}$ drawn at a scale of $1:25$. The actual space available for the shed

1. **Problem Statement:** List three real-life examples for each solid shape: cube, rectangular prism, square pyramid, cylinder, cone, sphere, and composite solids.

1. Problem: Given $\angle xOy = 60^\circ$, $A \in Ox$, and $Ay' \parallel Oy$ inside $\angle xOy$. $Ot$ and $At'$ are bisectors of $\angle xOy$ and $\angle xAy'$ respectively. 2. F

1. **Problem statement:** Given triangle $ABC$ with $\angle ABC = 70^\circ$, $\angle ACB = 65^\circ$, and a line $MN$ passing through points $M$ on $AB$ and $N$ on $AC$ such that $

1. Find the scale factor. Given two triangles with sides 6, 8, 10 and 12, 16, 20.

1. **Câu 16: Tính $\overrightarrow{SM} \cdot \overrightarrow{CB}$ trong hình chóp $S.ABCD$** - Bài toán cho hình chóp $S.ABCD$ với tất cả các cạnh bên và cạnh đáy đều bằng $a$.

1. **Problem statement:** We have a circle $\omega$ with radius 1. A collection $T$ of triangles is called good if: - Each triangle in $T$ is inscribed in $\omega$.

1. Bài toán yêu cầu chứng minh hai đường thẳng song song và xác định các cặp góc so le trong (slt) và đồng vị (đv). 2. Khi hai đường thẳng cắt nhau bởi một đường thẳng thứ ba (gọi