📐 geometry

1. **State the problem:** We have a right triangle with two 45° angles, meaning it is an isosceles right triangle (45°-45°-90° triangle). The hypotenuse is given as $7\sqrt{3}$, an

1. **Problem statement:** Given a circle with center O, tangent FE at point E, and points D and G on the circle such that EG = GF. Angle FÊG is $x$. We need to:

1. The problem is to find the area of a right triangle with legs measuring 8.9 cm and 8.1 cm. 2. The formula for the area of a right triangle is:

1. **Problem statement:** Calculate the angles:

1. نبدأ ببيان المسألة: لدينا مثلث به نقاط D و E و F و G و H، معطى أن DE = 8 سم، EH = 2 سم، EF = 6 سم، FG = 10 سم، والزوايا عند H و G قائمة. 2. المطلوب هو حساب النسبة (EF) // (HG) أ

1. Задачата: Имаме правоаголник ABCD каде што BC=2\cdot AB. Точката P е на страната AD така што AD=BP. Треба да најдеме големината на аголот \angle CPD. 2. Запишуваме што знаеме: В

1. **Problem Statement:** We need to determine which additional information is sufficient to prove that triangle $ABC$ is congruent to triangle $EBD$ given that lines $m$ and $n$ a

1. **State the problem:** We have a right square pyramid with a total surface area of $100 + 20\sqrt{146}$ square inches, including a base area of 100 square inches. We need to fin

1. **State the problem:** We have a board 104 inches long resting on a brace 22.5 inches high and 63 inches from the base of the board on the ground. We want to find how high the t

1. **State the problem:** We have an equilateral triangle inscribed in a circle with radius $8$ inches. We need to find the area inside the circle but outside the triangle, rounded

1. **State the problem:** We have triangle LMN with vertices L(1, -2), M(3, 0), and N(2, -3). We want to perform a dilation with scale factor $k=5$. 2. **Formula for dilation:** To

1. **State the problem:** We have quadrilateral STUV with vertices S(-5,7), T(-4,7), U(-2,1), and V(-8,1). We want to find the coordinates of these points after a 180° rotation abo

1. **Problem statement:** Rotate rhombus ABCD with vertices A(1,0), B(6,-2), C(8,-7), and D(3,-5) by 90° counterclockwise about the origin. 2. **Formula for 90° counterclockwise ro

1. **State the problem:** We have triangle RST with vertices \(R(0,6)\), \(S(6,7)\), and \(T(8,1)\). We want to find the coordinates of the vertices after a 180° rotation about the

1. **State the problem:** We have a rectangle WXYZ with vertices W(-8, -4), X(-2, -1), Y(0, -5), and Z(-6, -8). We need to find the coordinates of these points after a 270° counter

1. **State the problem:** We have quadrilateral MNOP with vertices M(1, 6), N(3, 4), O(4, -1), and P(-2, 3). We want to find the new coordinates of each vertex after applying the t

1. **State the problem:** We have trapezoid PQRS with vertices P(-7, -2), Q(-4, -1), R(-2, -5), and S(-8, -7). We need to find the coordinates of the reflected trapezoid P'Q'R'S' a

1. **State the problem:** We have a parallelogram GHIJ with vertices G(1, 5), H(8, 7), I(7, 3), and J(0, 1). We need to find the coordinates of the parallelogram after reflecting i

1. The Vertical Angle Theorem states that when two lines intersect, the pairs of opposite angles formed at the intersection are equal in measure. 2. To visualize this, imagine two

1. The Vertical Angle Theorem states that when two lines intersect, the opposite (or vertical) angles formed are equal. This means that if two lines cross each other, the angles th

1. **State the problem:** We need to use the parallelogram side theorem and ASA (Angle-Side-Angle) congruence criterion to find congruent triangles in a parallelogram and then prov