📐 geometry

1. The problem asks to complete the drawings using the line of symmetry marked by the dashes. 2. A line of symmetry means that one side of the shape is a mirror image of the other

1. **Problem Statement:** Given two wedges joined together, find the resultant wedge angle or combined effect.

1. **Problem statement:** In rectangle MNPQ, one vertex lies on the circle, and two vertices lie on the diameter of the circle. Given $MN=4$ and $MQ=6$, find $QL$. 2. **Understandi

1. The problem states the Pythagorean theorem: $x^2 + y^2 = z^2$. 2. This formula relates the lengths of the sides of a right triangle, where $x$ and $y$ are the legs and $z$ is th

1. **State the problem:** We need to determine which information can be used to prove that triangle ABC is congruent to triangle DEF. 2. **Given information:**

1. The problem asks to find the area of a shape with given dimensions 5, 4, and 1 square units. 2. Since the problem does not specify the shape, we assume it is a rectangle or a co

1. **State the problem:** Find the area of a parallelogram with base $7$ cm and height $3$ cm. 2. **Formula:** The area $A$ of a parallelogram is given by the formula:

1. **Problem Statement:** Construct triangle PQR where $PQ=4.5$ cm, $QR=5.2$ cm, and angle $PQR=45^\circ$. 2. **Formula and Rules:** To construct a triangle given two sides and the

1. **State the problem:** Find the distance between points $A(2,5)$ and $B(4,9)$ using the distance formula. 2. **Distance formula:** The distance $d$ between two points $A(x_1,y_1

1. **Problem statement:** Find the length of the side marked $x$ in each right triangle given the angle and one side. 2. **Key formulas and rules:**

1. **Problem statement:** We have a square-based pyramid with base ABCD where side AD = 19 cm.

1. **Problem statement:** We need to find the length of segment $HD$ in the given geometric figure with points $O, H, P, D, I$ and given lengths $OH=6$, $PD=9$, and $PI=27$. 2. **U

1. **Problem statement:** Given points A(2,3), B(-1,-4), and C(0,-2), find: a. The distance |AB|

1. Muammo: To‘rtburchak A(2; 2\sqrt{3}), B(5; 5\sqrt{3}), C(9; 3\sqrt{3}), D(3; \sqrt{3}) nuqtalarida berilgan. \n\n a) \sin \beta ni toping, bu yerda \beta = \angle BAD. \n\n b) A

1. **Stating the problem:** POR and QOR form a linear pair, meaning their angles add up to 180 degrees. Given that $a - b = 80$, find the values of $a$ and $b$. 2. **Formula and ru

1. Problem statement: Given a quadrilateral ABCD with vertices A(2, 2\sqrt{3}), B(5, 5\sqrt{3}), C(9, 3\sqrt{3}), and D(3, \sqrt{3}), find (a) \sin \beta where \beta = \angle BAD,

1. **State the problem:** We have an isosceles triangle ABC with AB = AC = 13 cm and BC = 10 cm. Points D and E lie on AC and AB respectively such that AD = AE = 6.5 cm, and ED is

1. **State the problem:** We want to find the largest area of a rectangle inscribed in a semicircle of radius 2. The rectangle's base lies along the diameter from $-x$ to $x$, and

1. **Problem statement:** A ship sails 20 km east from port P, then 25 km south, then 30 km east to reach point Q. 2. **Find the total distance sailed from P to Q:**

1. **Problem statement:** Find the angle between the line segments AB and AC where \(A=(2,3)\), \(B=(-1,-4)\), and \(C=(0,-2)\). 2. **Formula used:** The angle \(\theta\) between t

1. **Problem statement:** Given a circle with center $O$ and diameter $QS$, and points $P$, $R$, $S$, and $T$ as described, with $PR = PS$, prove that $$2TO \cdot QR = QS \cdot QT.