📐 geometry

1. The problem is to determine if Timo made an error in concluding that quadrilaterals LMNR and PQNO are not similar because no sequence of rigid transformations and dilations can

1. The problem asks to identify the error in Bastian's conclusion that quadrilateral OPQR is similar to quadrilateral ONML because he used a sequence of rigid transformations and d

1. **State the problem:** Given a right triangle with one angle measuring 35° and the side adjacent to this angle is 10 units long, find the length of the hypotenuse $x$. 2. The tr

1. **Problem statement:** In triangle (a), find the length $x$ in cm. The triangle is right-angled with an angle of 30°. 2. **Identify the sides:** The length 6 cm is adjacent to t

**Exercice 9 : Expression de \(\overrightarrow{AM}\) en fonction de \(\overrightarrow{AB}\) et \(\overrightarrow{AC}\)** 1. **Cas a)** \(\overrightarrow{AM} = -2 \overrightarrow{BC

1. Problem statement: We need to prove the following relation involving segments of a cyclic quadrilateral ABCD with additional constructions: $$\frac{BE \cdot AH}{GH} = \frac{ED \

1. **Problem statement:** We have a right triangle with a hypotenuse of 105 ft making a 30° angle with the horizontal. The vertical side (height of the tower) is 85 ft, and a man s

1. **Nêu bài toán:** Cho tam giác ABC cân, các đường trung tuyến BM, CN cắt nhau tại G. Trên BG lấy điểm E là trung điểm của BG, trên CG lấy điểm F là trung điểm của CG. Yêu cầu:

1. **Problem 14:** In parallelogram ABCD, point P lies on CD such that AD = DP = PC. (i) To prove AP bisects \(\angle A\):

1. Problem: In the figure with circle and tangents, AC is tangent to the circle, BE is parallel to CD, and given angles are (a) $\angle ABE = 42^\circ$, $\angle BDC = 59^\circ$. Fi

1. **Problem 1:** Find the volume and total surface area of a right prism with bases 12 cm apart and equilateral triangular base with side 6 cm. 2. The height (distance between bas

1. Problem (i): Find the measure of \(\angle BOD\) in figure (ii).\nGiven vertical angles at intersection O, \(\angle BOD\) is opposite to the given \(80^\circ\) angle \(\angle AOC

1. Problem (18): The perimeter of a triangular field is 144 m and its sides are in the ratio 3 : 4 : 5. Find the area of the field. Step 1: Let the sides be $3x$, $4x$, $5x$. Since

1. The problem is to understand the basic properties and equations related to circle geometry. 2. A circle is defined as the set of points equidistant from a fixed point called the

1. **State the problem:** Determine the type of triangle ABC formed by points A(2,1), B(5,7), and C(8,4) by calculating the lengths of its sides. 2. **Find the length of side AB:**

1. **Problem statement:** We have a parallelogram ABCD with points O(1,0), A(2,5), B(8,8), C(11,5) and F inside it such that segment AF is perpendicular to OC. We want to verify th

1. The problem asks to translate a given triangle on the coordinate plane 4 units to the right and 1 unit down. 2. Translation means shifting every point of the figure by the same

1. The given equation is the Pythagorean theorem: $a^2 + b^2 = c^2$. 2. This theorem applies to right triangles, stating that the square of the hypotenuse ($c$) equals the sum of t

1. **State the problem:** We have a cylinder with radius $r = 3$ cm and volume $V = 250$ cm$^3$. We need to find the height $h$ of this cylinder. 2. **Recall the formula for the vo

1. **Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°.** - The formula for the area of a sector is $$Area = \frac{\theta}{360} \times \pi r^2$$ w

1. The problem describes a semicircle with a radius of 7.2 meters and a horizontal diameter of 7.2 meters. This indicates possibly a misunderstanding since the diameter should be t