📐 geometry

1. The problem asks for the expression for the perimeter of a parallelogram with side lengths $s$ and $w$. 2. The perimeter $P$ of any parallelogram is the sum of the lengths of al

1. **State the problem:** We have two similar quadrilaterals KLMN and OPRS. We know the lengths of sides NK = 17, ML = 27, SO = 55, and we need to find the length of side PR. 2. **

1. **Problem Statement:** We have two similar triangles, JKL and MNO. We know sides LK = 5, KJ = 2 in triangle JKL, and side ON = 16 in triangle MNO. We need to find the length of

1. The problem asks us to find the new coordinates of the vertices of a square after a translation 3 units to the right and 8 units down. 2. The original vertices are given as:

1. **Problem Statement:** Find the azimuths of the lines AB, BC, CD, and DA given the angles at vertices A, B, C, and D. 2. **Understanding Azimuths:** Azimuth is the angle measure

1. **Problem Statement:** Find the azimuths of lines AB, BC, CD, and DA given angles between these lines and cardinal directions at points A, B, C, and D. 2. **Understanding Azimut

1. **State the problem:** We have a room with dimensions 5.8 m (length), 3.9 m (width), and 2.43 m (height). There are windows and doors with given dimensions. We need to find the

1. **Problem Statement:** Given a quadrilateral NOPQ where $m\angle N = m\angle P$ and $m\angle O = m\angle Q$, we want to analyze the properties of this quadrilateral. 2. **Unders

1. **Problem Statement:** Identify the quadrilateral CDEF given that $\overline{CD} \parallel \overline{EF}$, $CD = EF$, and the diagonals $\overline{CE}$ and $\overline{DF}$ are p

1. **Problem Statement:** Identify the type(s) of quadrilateral CDEF given that all sides are equal ($CD = DE = EF = FC$) and the diagonals are equal in length ($CE = DF$). 2. **Ke

1. **Problem Statement:** We are given a quadrilateral OPQR with diagonals OQ and PR intersecting at point S such that OS = SQ and PS = SR. 2. **Understanding the problem:** The co

1. Let's explore problems involving areas related to circles. 2. The area $A$ of a circle with radius $r$ is given by the formula:

1. The problem involves calculating the perimeter $p$ of a shape with radius $R$ and given constants: $\pi = 3.14$, $\sqrt{3} = 1.7$, and a cost rate of 0.35 per cm². 2. Since the

1. **Problem 13:** A round table cover has six equal designs. The radius of the cover is 28 cm. Find the cost of making the designs at the rate of 0.35 per cm². Use \( \sqrt{3} = 1

1. **Problem Statement:** We are given a quadrilateral STUV with the following properties: - $ST \cong UV$

1. The problem asks to find the translation rule that maps triangle $\triangle CDE$ to triangle $\triangle C'D'E'$.\n\n2. A translation moves every point of a figure the same dista

1. **State the problem:** We have triangle △VWX with vertices V(-10, 2), W(-7, 8), and X(-3, 2), and its translation △V'W'X' with vertices V'(4, -8), W'(7, -2), and X'(11, -8). 2.

1. **Problem statement:** Given a triangle with sides 38, 33, and an angle of 35° at vertex A adjacent to side 38, find the angle A and the length of side $x$ opposite the 35° angl

1. **Red: Reflect square STUV in the x-axis** The reflection rule in the x-axis is $(x,y) \to (x,-y)$.

1. **State the problem:** Locate each group of points on a Cartesian plane and join the points in each group separately.

1. The problem asks to write the coordinates of each point labeled A through I on a Cartesian coordinate plane. 2. The Cartesian plane has an x-axis (horizontal) and y-axis (vertic