📐 geometry

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.

1. **Problem Statement:** Given angles a, b, c, d, e with some known values and a statement about angles b and f, find the missing angles and verify Theo's claim.

1. **Stating the problem:** We have a triangle ABC with sides $AB=3.6$ cm and $AC=4.3$ cm. Points D and E are defined such that $\vec{AD} = 2\vec{AB}$ and $\vec{DE} = 3\vec{BC}$. W

1. **State the problem:** We have a cylinder with circular faces each having a circumference of 76 mm. The distance from the center of one circular face to the edge of the other ci

1. **Problem statement:** We have a square-based pyramid with a base side length of 6 cm and triangular faces with slant height 11 cm. We need to find the vertical height of the py

1. **Problem Statement:** Determine if triangle $\triangle NMB$ is semi-equilateral given the angles and side lengths in $\triangle ANB$ and the geometric relationships described.

1. **Problem statement:** Given a semicircle with diameter $AB$ and center $O$ where $OB=4$ cm, point $N$ lies on the semicircle such that $\angle NBA=30^\circ$. Tangents at $N$ an