📐 geometry

1. **State the problem:** We need to find the perimeter of a right triangle with legs of lengths $\sqrt{27}$ cm and $\sqrt{3}$ cm. 2. **Recall the formula:** The perimeter $P$ of a

1. **State the problem:** We have a trapezium with area $6\sqrt{21}$ cm², a top side of 5 cm, a height of $\sqrt{7}$ cm, and a base labeled $f$ cm. We need to find $f$ in the form

1. **Problem Statement:** We have triangle $\triangle ABC$ with vertices $A(-11, 2)$, $B(3, -5)$, and $C(6, 1)$. We need to:

1. **Problem Statement:** Calculate various properties of triangle $\triangle ABC$ with vertices $A(-11,2)$, $B(3,-5)$, and $C(6,1)$.

1. **Problem statement:** We are given a straight horizontal line with two angles adjacent to it: one is 50° on the left side, and the other is 35° on the right side. We need to fi

1. **Problem Statement:** We have a right triangle with legs 24 and $x$, and the hypotenuse divided into two segments of lengths 12 and 18. We need to find the value of $x$. 2. **U

1. Muammo: faqat to'g'ri burchakli uchburchaklar haqida gaplashamiz. 2. To'g'ri burchakli uchburchakda bitta burchak $90^\circ$ ga teng.

1. **Problem Statement:** Identify the type of angle pairs in each diagram (8 to 15) as corresponding, alternate interior, alternate exterior, same-side interior, vertical, or line

1. **State the problem:** We need to prove that two lines are parallel when they are cut by a transversal. 2. **Key concept:** When a transversal cuts two lines, certain angle pair

1. **Problem Statement:** We have two triangles, △ABC and △A'B'C', where △A'B'C' is a scaled copy of △ABC. We know the sides of △ABC: AB = 5, BC = 2, AC = 6, and the sides of △A'B'

1. **Problem Statement:** A solid cylinder has radius 18 cm and height 15 cm. A conical hole of radius $r$ cm and depth 12 cm is drilled on one end. The volume of the material remo

1. **Problem Statement:** We have a 30-inch by 16-inch piece of cardboard. Squares of side length $x$ are cut from each corner, and the sides are folded up to form an open box. We

1. **Problem Statement:** Given two parallel lines AB and CD, with angles \(\angle BNO = 128^\circ\) and \(\angle COM = 56^\circ\), find \(\angle MON\) and \(\angle DON\).\n\n2. **

1. **Problem Statement:** Determine the truth value of the following statements based on the given 3D figure with two parallelograms (planes) and points labeled as described. 2. **

1. **Problem Statement:** Determine the position of the given line relative to coordinate axes or other reference lines. 2. **Key Concepts:** The position of a line in 3D or 2D spa

1. **Homework 1: Determine if two lines are perpendicular, skew, or intersecting** - Problem: Given two lines in 3D or 2D space, determine if they are perpendicular, skew, or inter

1. **Stating the problem:** Given a circle with center P, angle $\angle BEC = 50^\circ$, angle $\angle EBC = 60^\circ$, and diameter $AD$ perpendicular to chord $EC$, find the meas

1. The problem is to create a graph with three vertical sections separated by two curved boundaries labeled "T" and "T-S" with sections labeled "1" and "T" as described. 2. To repr

1. **Problem:** Find the midpoint of the line segment joining the points $(-6, 2)$ and $(4, -8)$. 2. **Formula:** The midpoint $M$ of a segment joining points $(x_1, y_1)$ and $(x_

1. **Problem Statement:** Find the distance between each pair of points given. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the dis

1. Պատկերացնենք, որ ունենք եռանկյուն ABC, որտեղ <B=62°, <A=78°. 2. Եռանկյան անկյունների գումարը միշտ հավասար է 180°-ի, հետևաբար <C = 180° - <A - <B = 180° - 78° - 62° = 40°: