📐 geometry

1. **State the problem:** We need to find the equation of the perpendicular bisector of a segment defined by points $P$ and $Q$. 2. **Formula and rules:** The perpendicular bisecto

1. Let's state the problem: You want to find the length of a side in a triangle given only an angle, but no other information. 2. Important note: To find the length of a side in a

1. **Problem statement:** We are given a circle with center $O$ and points $P$ and $Q$ on the circumference. The central angle $\angle POQ$ is $280^\circ$. We need to find the angl

1. **Stating the problem:** We have a right triangular prism shaped ramp with dimensions: base length $20$ ft, vertical height $12$ ft, side height $8.5$ ft, and diagonal ramp leng

1. **Problem:** Find the total surface area of the ramp. 2. **Given:** Ramp dimensions include a length of 170 ft and a width of 12 ft.

1. **Énoncé du problème :** Nous avons un segment $DE$ avec $D(5,6)$ et $E(5,11)$.

1. **State the problem:** We need to identify the conditions that guarantee a quadrilateral is a parallelogram and solve for angles and lengths in quadrilateral CUTE given various

1. **Problem statement:** Find the image of the curve given by the equation $$x + 2y = 2$$ after a dilation centered at the origin $(0,0)$ with a scale factor of $\frac{1}{2}$.

1. The problem asks for the conditions that guarantee a quadrilateral is a parallelogram. 2. One key property of parallelograms is that their opposite sides are equal and parallel.

1. **Stating the problem:** Complete the table for polygons with given sides, sum of interior angles, and measurement of each angle for regular polygons.

1. **State the problem:** We have a polygon with 7 vertices and interior angles labeled 79°, 85°, 72°, 66°, 91°, and one unknown angle $x$. We need to find the value of $x$. 2. **F

1. **State the problem:** We are given a polygon with five interior angles measuring 65°, 88°, 152°, 96°, and an unknown angle $x$. We need to find the value of $x$. 2. **Formula u

1. **Stating the problem:** We have a pentagon with some external and internal angles given. The external angles are 255 degrees (top-left vertex) and 26 degrees (top-right vertex)

1. **State the problem:** We have a seven-sided polygon (heptagon) with six known interior angles: 117°, 101°, 138°, 110°, 123°, and one unknown angle $x$. We need to find the valu

1. The problem asks to find the value of the angle $x$ in a quadrilateral where the other interior angles are given as 81°, 95°, 42°, and 111°. 2. Recall the important rule: The su

1. **State the problem:** We need to find the volume of a 3D solid shaped like a large "I". It consists of three rectangular parts: two horizontal parts (top and bottom) and one ve

1. **Problem Statement:** We need to identify and mark two types of angles based on the diagrams and descriptions given:

1. **Problem Statement:** Mark the angles described in the diagrams:

1. **Problem Statement:** Identify which of the given nets (A, B, C, D) are valid nets of a hexagonal prism. 2. **Understanding a Hexagonal Prism:** A hexagonal prism has 8 faces:

1. The problem asks to identify which nets correspond to a heptagonal prism. 2. A heptagonal prism is a 3D solid with two parallel heptagon bases and rectangular faces connecting c

1. **Stating the problem:** We are given several angle relationships involving vertically opposite angles, alternate angles, and angles formed by parallel lines and a transversal.