📐 geometry

1. **Problem Statement:** We have a triangle $ABC$ with an exterior point $T$ on the extension of side $AC$. The angles are given as follows: - Angle at $B$ is $70^\circ$.

1. **Problem Statement:** Determine how angles $\angle BOC$ and $\angle COD$ are related given the described intersecting lines and rays at point $O$. 2. **Understanding the Angles

1. **State the problem:** We are given that $\overline{AC} \perp \overline{BD}$ and need to complete the flowchart proof showing congruence between triangles $\triangle ABD$ and $\

1. **Problem Statement:** We are given a triangle with vertices $A(-5, -6)$, $B(0, -6)$, and $C(0, -10)$.

1. **State the problem:** We need to find the coordinates of the vertices of triangle $FGH$ after a dilation with scale factor $2$ centered at the origin. 2. **Recall the dilation

1. **Problem Statement:** We are given a wall thickness of $6\text{mm}$ on the top and bottom, and $12\text{mm}$ on the sides.

1. **Problem Statement:** We have a regular decagonal prism with each side of the decagon base measuring $2$ cm and the height of the prism $8$ cm.

1. **State the problem:** We need to find the surface area of a triangular prism with an isosceles triangular base. 2. **Identify the shapes in the net:** The net consists of 3 rec

1. **State the problem:** Calculate the volume of a tank using the formula given. 2. **Formula used:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the r

1. **State the problem:** We need to find the surface area of a cylinder with height $H = 2000\text{mm}$ and diameter $D = 1000\text{mm}$. We will convert dimensions to meters for

1. **State the problem:** Calculate the volume of concrete needed for a driveway slab that is $200\text{mm}$ deep, using the surface area of the top of the driveway. 2. **Given dim

1. **State the problem:** We need to find the volume of a cube with side lengths of $2000\text{ mm}$ each. 2. **Formula for volume of a cube:**

1. **State the problem:** We need to find the area of a triangular roof truss with base $2000\text{mm}$ and height $1000\text{mm}$. 2. **Formula for the area of a triangle:**

1. **Problem Statement:** We are given the point $ (0,4) $ and asked where it is located. 2. **Understanding Coordinates:** A point in the coordinate plane is given as $ (x,y) $, w

1. The problem asks us to determine the location of the point $(0,4)$ on the coordinate plane. 2. Recall the definitions:

1. **State the problem:** We need to find the length of the wire $n$ that connects the top of a telegraph pole to a point 3 m from its base. 2. **Identify the shape and theorem:**

1. **Problem statement:** We have a right-angled triangle $XYZ$ with the right angle at $Y$. The side $XY$ is $5$ cm, the hypotenuse $XZ$ is $17$ cm, and we need to find the length

1. **State the problem:** We need to find the volume $V$ of a cylinder with radius $r = 2$ m and height $h = 7$ m. 2. **Formula:** The volume of a cylinder is given by

1. **State the problem:** We need to find the volume $V$ of a cylinder with radius $r = 5$ cm and height $h = 6$ cm. 2. **Formula:** The volume of a cylinder is given by $$V = Bh =

1. **State the problem:** We have a right triangle with vertices $A$, $B$, and $C$, where angle $C$ is the right angle ($90^\circ$), and angle $A$ measures $55^\circ$. We need to f

1. **State the problem:** We are given a triangle with angles $C = 33^\circ$ and $B = 70^\circ$. We need to find the measure of angle $A$. 2. **Recall the triangle angle sum rule:*