📐 geometry

1. Problem statement: In the parallelogram $ABCD$, $AB=10$ cm, $AD=7$ cm and $\angle DAB=60^\circ$.\n 2. Diagram suggestion: Place $A$ at the origin, let $AB$ lie on the positive $

1. **Problem Statement:** We have a quadrilateral ABCD with opposite sides parallel (AB \parallel DC and AD \parallel BC). Angles at vertices A, B, D are $x^\circ$, $y^\circ$, and

1. **Problem statement:** Given triangle ABC with point D on side BC, angles \(\angle DAC = \angle BAD\), and lengths \(AC = 6.5\), \(CD = 3.4\), and \(AB = 4.9\), find the length

1. **Stating the problem:** We have a square with two diagonal lines intersecting inside it, creating two triangles. We know two angles: 40° at the top-left corner and 80° near the

1. **Stating the problem:** We have a square with four right angles (each 90°). Inside the square, there are angles 40°, 80°, and an unknown angle $x$°. 2. **Understanding the prob

1. **Problem Statement:** We have a square ABCD with vertices A(3,1), B(3,6), C(8,1), and D(8,6).

1. **Problem Statement:** Calculate the size of the marked angles in problem 2a, which is a square divided by two diagonals forming four angles labeled $\alpha$, $b$, $e$, and $d$.

1. The problem asks for the scalar factor given that the image length $A'$ is 15 units. 2. The scalar factor (scale factor) is the ratio of the image length to the original length.

1. **State the problem:** We have two similar triangles on the coordinate plane, triangle A with vertices at approximately $(-8,6)$, $(-2,6)$, $(-5,7.5)$ and triangle A' with verti

1. The problem is to understand how to find the scale factor between two similar figures. 2. The scale factor is the ratio of any two corresponding lengths in the two figures.

1. **Stating the problem:** We have two triangles, A and A', on the coordinate plane. Triangle A is smaller with vertices approximately at $(-5,6)$, $(-2,6)$, and $(-5,4)$. Triangl

1. **State the problem:** We have two right triangles inside a larger triangle. The left triangle has one leg of length 4 and a hypotenuse of length 10. The right triangle has one

1. نبدأ بتحديد إحداثيات النقطة G المعطاة بالمرجع {(A; -2); (B; 1); (C; -1)} حيث A(1;0), B(-3;2), C(1;3). صيغة إحداثيات G هي:

1. **بيان المسألة:** لدينا مثلث ABC ونقطة مرجعية G_k معرفة بالمعاملات {(A؛ k)،(B؛ −1)،(C؛ 1)} حيث k عدد حقيقي.

1. **بيان المسألة:** لدينا مثلث ABC ونريد دراسة المرجع $G_k$ المعرف بالمعاملات $k$، $-1$، و$1$ على التوالي للنقاط $A$, $B$, و$C$.

1. **Problem Statement:** Calculate the radius $x$ for sectors with given areas and central angles (Question 4). 2. **Formula:** The area $A$ of a sector with radius $r$ and centra

1. **Problem:** The curved surface area (CSA) of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder. 2. **Formula:** The curved surf

1. **بيان المسألة:** لدينا مثلث ABC ونقاط A' و B' و C' معرفة بعلاقات متجهية:

1. **بيان المسألة:** لدينا مثلث ABC متساوي الأضلاع حيث $\alpha = AB = AC = BC$، ونريد دراسة مجموعة النقاط $\Gamma$ التي تحقق:

1. **State the problem:** Find the radius of a sector, the perimeter of the flower bed, and the area of the flower bed based on given dimensions.

1. **Problem Statement:** We are given a parallelogram with angles labeled as $44^\circ$, $52^\circ$, $y^\circ$, $x^\circ$, and $97^\circ$. We need to find the values of $x$ and $y