📐 geometry

1. **Problem Statement:** Determine if each triangle is acute-angled or obtuse-angled using the side lengths given. 2. **Formula and Rule:** Use the Law of Cosines or compare squar

1. **State the problem:** We have a rectangle AOBC with vertices A(0,3), O(0,0), and B(5,0). We need to find the length of its diagonals. 2. **Identify the fourth vertex:** Since A

1. **State the problem:** We need to show that the points $(0,1)$, $(1,4)$, $(4,3)$, and $(3,0)$ are vertices of a square. 2. **Formula and rules:** To prove points form a square,

1. **Problem:** Write the six elements (3 sides and 3 angles) of $\Delta ABC$. - The three sides are $AB$, $BC$, and $CA$.

1. **Problem 3: Find A, B, and C** Given two parallel lines cut by a transversal, the angles A, B, and C are related by the properties of parallel lines and transversals.

1. **Problem Statement:** The Pythagoras theorem states a fundamental relation in a right-angled triangle between the lengths of the sides.

1. **State the problem:** We need to find a series of transformations that map Figure R with vertices $(-8,6)$, $(-6,4)$, $(-1,3)$, and $(-1,5)$ onto Figure S with vertices $(1,0)$

1. **State the problem:** We need to find a series of transformations that map Figure K with vertices at $$(-9,9), (-1,9), (-3,4), (-3,1), (-9,4)$$ onto Figure L with vertices at $

1. **State the problem:** The Pythagorean theorem helps us find the length of a side in a right triangle. 2. **Formula:** The theorem states that in a right triangle, the square of

1. **Problem 1:** Given $NO = 17$ and $NP = 5x - 6$, find $x$, then find $NP$ and $OP$. - Assume points $N$, $O$, and $P$ are collinear with $O$ between $N$ and $P$, so $NP = NO +

1. **Problem statement:** We have a right triangle $\triangle ABC$ right-angled at $A$. $D$ is the midpoint of the altitude $AH$ from $A$ to $BC$. The perpendicular bisector of $AB

1. **Énoncé du problème** : Nous avons un triangle non aplati $ABC$ et deux points $M$ et $N$ définis par les vecteurs:

1. The problem involves analyzing a square grid with a diagonal and shaded regions. 2. The diagonal line runs from the bottom-left corner to the top-right corner, dividing the squa

1. **State the problem:** We are given a beam of light striking a mirror at point $B$. The angle of incidence $\angle ABC$ is $39^\circ$. We need to find the angle of reflection an

1. **Nyatakan masalah:** Kita diberi sebuah kuboid dengan lebar dan tinggi yang sama, dan panjangnya dua kali ganda lebarnya. Jumlah luas permukaan bentangan (net) kuboid itu ialah

1. **State the problem:** We have three rectangular tanks A, B, and C. Tank A is initially filled to 3/5 of its height with water. Water flows from tank A to tank B, then to tank C

1. **State the problem:** We need to find the area of a symmetric house-like polygon composed of a rectangular body and a peaked roof. 2. **Identify the dimensions:** The numbers g

1. **Stating the problem:** We have a symmetric house-like shape composed of a peaked roof, a rectangular body, and semicircular bulges on both sides. The given numbers likely repr

1. Bài toán yêu cầu tính góc $BMC$ trong một hình học nào đó. 2. Công thức tính góc $BMC$ phụ thuộc vào vị trí các điểm $B$, $M$, và $C$ trong hình.

1. **Nêu vấn đề:** Chúng ta cần xác định xem góc $BMC$ chắn cung $BC$ có phải là góc vuông theo tính chất góc tạo bởi tiếp tuyến và dây cung hay không.

1. **Đề bài:** Cho tam giác $ABC$ ngoại tiếp đường tròn $(I)$, nội tiếp đường tròn $(O)$. Đường tròn $(I)$ tiếp xúc với các cạnh $BC$, $AC$, $AB$ lần lượt tại $D$, $E$, $F$. Đường