📐 geometry

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

1. **Problem statement:** Find the vertices of the triangle invariant under two transformations:

1. Problem 14: Given a figure with BC = 4, AB = 6, AD = 3 units, and \(\angle AEC = 90^\circ\), find the length of EC. 2. Since \(\angle AEC = 90^\circ\), triangle AEC is a right t

1. The problem involves performing dilations on points or shapes with given centers and scale factors $k$. 2. The dilation formula for a point $P(x,y)$ with center $C(x_c,y_c)$ and

1. **Stating the problem:** We have a triangle with a perpendicular dropped from the top vertex to the base, splitting the base into two segments of lengths 50 and 46 units. The si

1. مسئله: تعداد مکعب‌های موجود در تصویر را پیدا کنیم. 2. برای حل این مسئله، باید مکعب‌ها را به صورت جداگانه بشماریم و توجه کنیم که مکعب‌های بزرگ‌تر ممکن است از ترکیب چند مکعب کوچک‌

1. مسئله: تعداد مکعب‌های موجود در تصویر را بیابیم. 2. برای حل این مسئله، باید تعداد مکعب‌های کوچک، متوسط و بزرگ را جداگانه بشماریم و سپس جمع کنیم.

1. مسئله: تعداد مکعب‌ها را پیدا کنید. 2. برای محاسبه تعداد مکعب‌ها، باید بدانیم مکعب‌ها چگونه چیده شده‌اند یا ابعاد ساختار مکعبی چیست.