📐 geometry

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

1. **State the problem:** We need to use the parallelogram side theorem and ASA (Angle-Side-Angle) congruence to find congruent triangles in a parallelogram and show that its diago

1. **Problem Statement:** Given two triangles ABC and A'B'C' on concurrent lines L, M, N meeting at point O, with AB \parallel A'B' and BC \parallel B'C', use Thales theorem to sho

1. **Problem Statement:** Given points A, B, C, A', B', C' on concurrent lines L, M, N meeting at point O, with AB \parallel A'B' and BC \parallel B'C', prove using Thales' theorem

1. **State the problem:** Find the area of the colored part of the figure in problem 3, which is a heart shape with a dimension labeled 5 cm.

1. The problem asks to find the value of angle $b$ in a triangle where two angles are given: $38^\circ$ and $101^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the in

1. **State the problem:** We have a circle with a secant line FED and a tangent line CD. Given the lengths CD = 43 and ED = 31, we need to find the length of FE. 2. **Recall the ta

1. **Énoncé du problème :** Soit un triangle FAL. On définit les points I, J, K par :

1. Masalah: Tentukan koordinat bayangan segitiga ABC dengan koordinat A(2,1), B(5,-1), dan C(4,3) oleh pencerminan terhadap sumbu Y (soal b). 2. Rumus pencerminan terhadap sumbu Y:

1. The problem involves a right triangle ABC with right angle at C, hypotenuse AB, and altitude CD drawn perpendicular to AB at D. 2. We are given three parts: