📐 geometry

1. The problem is to understand and identify alternate interior angles in a diagram involving two parallel lines cut by a transversal. 2. Alternate interior angles are pairs of ang

1. **Problem Statement:** Count the number of triangles in the given geometric figure. 2. **Understanding the figure:** The figure is a large triangle with vertices at bottom-left

1. **Problem Statement:** Given a circle with center O and diameter AB, OD is parallel to AC, and EF is the tangent at D. Angle $B\hat{C}D = x^\circ$. We need to find angles $B\hat

1. Bạn yêu cầu vẽ hình nhưng không cung cấp chi tiết về hình cần vẽ. 2. Vui lòng cung cấp thêm thông tin về loại hình hoặc phương trình bạn muốn vẽ để tôi có thể giúp bạn chính xác

1. **Nêu bài toán:** Tính chiều dài đoạn dây văng dài nhất của cầu Cần Thơ, biết chiều cao trụ tháp từ mặt nước là $175,30m$, khoảng cách từ mặt nước đến mặt cầu là $30m$, và chiều

1. **Problem statement:** Given a right triangle $ABC$ with right angle at $A$, point $M$ lies on hypotenuse $BC$. Points $D$ and $E$ are the feet of perpendiculars from $M$ to $AB

1. The problem is to find the values of angles $x$, $y$, and $z$ given the angles $40^\circ$, $121^\circ$, and the variables $x^\circ$, $y^\circ$, $z^\circ$. 2. We use the rule tha

1. **State the problem:** Jessica's eyes are 175 cm above the floor. She places a mirror on the ground 650 cm away from a flagpole. She then walks back 1 meter (100 cm) until she s

1. **State the problem:** Calculate the distance $d$ between two points using the distance formula. 2. **Distance formula:** The distance between points $(x_1, y_1)$ and $(x_2, y_2

1. **State the problem:** We are given a sector OAB of a circle with radius $r = 4.6$ mm and sector area $A = 18$ mm². We need to find the central angle $\theta$ in degrees to 1 de

1. **Stating the problem:** We are given a trapezoid IJKL with two bases IJ and LK expressed in terms of $x$, and a median MN with length 15. We need to find the value of $x$ and t

1. **Stating the problem:** Identify which two lines among m, n, o, p, and q are parallel based on the given figure and definitions. 2. **Definition:** Parallel lines are lines in

1. **State the problem:** We need to find the area of the minor sector OAB of a circle with radius $40$ cm and central angle $36^\circ$. 2. **Formula for the area of a sector:** Th

1. **Problem statement:** Given a circle with diameter QIT and angles \(\angle QIT = 48^\circ\), \(\angle TQR = 70^\circ\), and \(\angle MCI = 17^\circ\), find the sizes of the fol

1. **Problem Statement:** We have a solid composed of a conical frustum with a hemispherical top. Given:

1. **Problem statement:** We have a solid made of a conical frustum with a hemispherical top. Given:

1. **Problem:** Find the length of the angle indicated for trapezoid 1, where angle at S is 65° and angle at R is unknown. 2. **Formula and rules:** In a trapezoid, consecutive ang

1. **State the problem:** We need to find the perimeter of an irregular polygon shaped like a rotated letter "E" with given side lengths. 2. **Identify the given sides:** The polyg

1. Stating the problem: Generate a similar exercise involving a composite figure made of a rectangle and two semicircles but with different measurements. 2. Original figure details

1. **Problem Statement:** We have a solid made of a conical frustum with a hemispherical top. Given:

1. The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$