📐 geometry

1. **State the problem:** We need to find the image of trapezoid PQRS after reflecting it over the line $y = -x$. 2. **Recall the reflection rule:** Reflecting a point $(x,y)$ over

1. **Problem Statement:** Reflect the kite TUVW with vertices \(T(6,-10)\), \(U(10,-4)\), \(V(6,4)\), and \(W(2,-4)\) over the line \(y = x\). 2. **Reflection Rule:** When reflecti

1. **State the problem:** We need to find the image of kite STUV after reflecting it over the vertical line $x = -2$. 2. **Recall the reflection rule:** When reflecting a point $(x

1. The problem asks which of the given shapes are always similar. 2. Let's recall the definitions:

1. Let's clarify the term "bisects." In geometry, to bisect means to divide something into two equal parts. 2. For example, a line segment bisector divides the segment into two equ

1. **Problem Statement:** We have a circle with center $P$ and diameter $\overline{AB}$. Points $A$, $B$, $C$, and $D$ lie on the circle in clockwise order. We know the central ang

1. **Problem Statement:** The problem asks about the relationship between the exterior bisector of the vertex angle of an isosceles triangle and its base.

1. The problem asks: "All ............... are similar." with options (a) triangles, (b) rectangles, (c) parallelograms, (d) squares. 2. Similar figures have the same shape but not

1. **State the problem:** We are given the circumference of a circle as 176 centimeters and need to find its radius. 2. **Formula used:** The circumference $C$ of a circle is relat

1. **Problem statement:** Given a circle with diameter CD, AE = 6 cm, and CE = 4 cm, find the radius length of the circle M. 2. **Recall the properties:** The diameter CD passes th

1. **State the problem:** Find the area of a square whose vertices lie on the circle given by the equation $$x^2 + y^2 - 4x + 6y + 4 = 0$$. 2. **Rewrite the circle equation in stan

1. **Find the unknown marked angle in each triangle.** The sum of angles in any triangle is always $180^\circ$.

1. The problem is to find the area of a rectangle. 2. The formula for the area $A$ of a rectangle is:

1. **State the problem:** We need to find the value of $y$ for the point $P = \left(-\frac{1}{7}, y\right)$ that lies on the unit circle centered at the origin. 2. **Recall the equ

1. **Problem statement:** Find the length of line segment PQ where P(-1,1) and Q(3,4). 2. **Formula used:** The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is given b

1. **Problem statement:** Find the length of line segment $PQ$ where $P(-1,1)$ and $Q(3,4)$. 2. **Formula used:** The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is giv

1. **Problem statement:** Calculate the area of trapezium ABCD, the perpendicular distance $h$ from point B to line AD, and angle DAB given:

1. **Problem statement:** Two trees stand on flat ground. The smaller tree is 7 m tall. The distance from the top of the smaller tree to the base of the taller tree is 15 m. The di

1. **Problem statement:** Find the measures of arcs and angles in a circle where given angles are 87° and 135°, and unknowns are $x$ and $y$. 2. **Relevant formulas and rules:**

1. **Problem statement:** Given the proportion $\frac{AC}{AE} = \frac{AB}{AD}$, prove that $ED \parallel CB$. 2. **Step 1: Identify the common angle.**

1. **Problem Statement:** Find the yellow area inside a square of side length 8, below the triangle formed by two radii of the inscribed circle meeting the bottom corners of the sq