📐 geometry

1. **State the problem:** We need to find the coordinates of the image R''S''T''U'' after reflecting the figure RSTU across the x-axis. 2. **Recall the reflection rule across the x

1. **State the problem:** We are given a triangle \(\triangle DEF\) with sides \(f = 830\) cm, \(d = 520\) cm, and angle \(\angle E = 129^\circ\). We need to find the length of sid

1. **State the problem:** Given that CA bisects \(\angle BAD\), \(AB \perp BC\), and \(AD \perp DC\), prove that \(\triangle ABC \cong \triangle ADC\). 2. **Identify given informat

1. **State the problem:** Given quadrilateral ABCD with AB \parallel CD and AC bisects BD, prove that BD bisects AC. 2. **Understand the given information:**

1. **Stating the problem:** We have a circle with center M and radius $r = 6370$ km. There is a sector formed by two radii with a central angle of $142^\circ$. We want to find the

1. **Problem Statement:** Find the area of the large semicircle given smaller semicircle and quarter circle inside it, each labeled with radius 4. 2. **Understanding the problem:**

1. **State the problem:** We want to calculate the area of a square. 2. **Formula:** The area $A$ of a square is given by the formula:

1. The problem involves understanding a circular arc centered at the fraction $\frac{1}{2}$ with a radius given by the fraction $\frac{2}{4}$.\n\n2. The center of the circle is at

1. **Problem Statement:** We have a cube net with faces labeled E, A, B, C, D, F arranged as shown:

1. **Stating the problem:** We are given a right triangle with sides 20 and 25, and a side $x$ opposite the right angle. We want to find the value of $x$.

1. Problem: Find the volume of a composite solid consisting of a hemisphere on top of a cube, each side of the cube is 8 cm. 2. Formulae:

1. **Problem statement:** We have two circles with centers O and P. Line segment RT is tangent to the larger circle at R and to the smaller circle at S. Given lengths are $OR=9$ m,

1. **Problem Statement:** Find the surface area of a solid formed by joining four cubes each with side length 25 cm in two different arrangements.

1. **Problem statement:** Given a square ABCD with side length 8, a smaller square is formed by joining the midpoints of each side of ABCD. We need to find the perimeter of this sm

1. **State the problem:** We need to find the capacity in millilitres of two containers:

1. **State the problem:** We are given a parallelogram PQSR with side lengths labeled as $PQ = (2x + 5)$ cm and $RS = (4x + 1)$ cm. We need to find the length of side $PQ$. 2. **Re

1. **Problem Statement:** We have a parallelogram LMNP with vertices L(-4,1), M(2,-4), N(3,-2), and P(-3,-1). We want to determine which additional information would prove LMNP is

1. **Problem 1: What additional information would prove that LMNP is a rectangle?** Given LMNP is a parallelogram, to prove it is a rectangle, we need to show that one angle is a r

1. **State the problem:** We need to prove that parallelogram KLMN is a rhombus using the given statements and coordinates of vertices: \(M(1,1)\), \(N(3,5)\), \(L(5,3)\), and \(K(

1. **State the problem:** We are given an isosceles trapezoid KLMN with side lengths KL = $2\sqrt{2}$, LM = $\sqrt{5}$, and MN = $\sqrt{2}$. We need to find the perimeter of trapez

1. **State the problem:** We need to find the perimeter of rhombus ABCD with vertices A(1,1), B(-2,-3), C(-5,1), and D(-2,5). 2. **Recall the properties of a rhombus:** All sides a