📐 geometry

1. **State the problem:** Determine which combination of figures among Figure 1, Figure 2, and Figure 3 are similar and explain why. 2. **Recall the definition of similar figures:*

1. **Stating the problem:** We need to find the size of angle $x$ in a triangle formed by two parallel lines and a transversal, with given angles $87^\circ$, $45^\circ$, and $36^\c

1. **State the problem:** We need to find the length of side $c$ in a right triangle where angle $B$ is $35^\circ$, side $BC$ (opposite angle $A$) is $16$ m, and angle $C$ is the r

1. The problem is to find the second longest side of a triangle given certain conditions. 2. To find the second longest side, we first need to identify all sides and their lengths.

1. **Stating the problem:** We have a quadrilateral ABCD with sides AB = 85 and AD = 35, and we want to find the angle at vertex A (\(\angle BAD\)). 2. **Understanding the triangle

1. The problem involves finding missing side lengths in various right triangles with given angles and side lengths. 2. We use the Pythagorean theorem and special right triangle rat

1. **State the problem:** We are given four vertices of a rectangle on the coordinate plane: $(-2, 1)$, $(2, 1)$, $(-2, -1)$, and $(2, -1)$. We want to understand the properties of

1. **State the problem:** We have a triangle with sides 10 cm, 13 cm, and 5 cm, and angles 40°, 90°, and $x^\circ$. We need to find the value of $x$ to 1 decimal place. 2. **Identi

1. **Problem statement:** (a) Given the scale of a map is 1 : 250000, and the actual distance between two cities is 80 km, calculate the distance on the map in centimetres.

1. **State the problem:** Find the coordinates of the center of the parallelogram with vertices A(-7, 5), B(6, 5), C(4, -2), and D(-9, -2). 2. **Formula used:** The center (or cent

1. The problem asks which property is true for all rectangles regarding their diagonals and sides. 2. Recall the definition and properties of rectangles:

1. **Problem statement:** We need to find the volume of material used to build a river bridge arch shaped like a downward-opening parabola. The bridge is 4 meters wide, with a span

1. **State the problem:** We need to find the volume of a three-dimensional rectangular prism composed of two connected rectangular sections. 2. **Identify dimensions:**

1. **State the problem:** Jenny claims the volume of the rectangular prism with dimensions 25 cm (length), 5 cm (height), and 2 cm (width) is 250 cubic centimeters because she calc

1. **State the problem:** Calculate the volume of a pentagonal prism with given edge lengths. 2. **Formula:** The volume $V$ of a prism is given by:

1. **State the problem:** Calculate the volume of a 3D shape that consists of a rectangular base and a triangular prism roof. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the volume of a 3D house-shaped figure composed of a rectangular base and a triangular prism roof. 2. **Identify the shapes and dimensions

1. Problem: Vi skal undersøge, om 10 liter maling kan være i en cylinderformet spand med radius og højde på 15 cm. 2. Formel: Volumen af en cylinder er $$V = \pi r^2 h$$ hvor $r$ e

1. **State the problem:** We need to find the volume of a sphere with diameter 6 units. 2. **Formula for the volume of a sphere:**

1. Problem: Vi skal finde ud af, om 10 liter maling kan være i en cylinderformet spand med radius $r=15$ cm og højde $h=15$ cm. 2. Formel: Volumen af en cylinder er givet ved $$V=\

1. **Problem:** Find the values of $x$ and $y$ in the first triangle where the hypotenuse is 20 and the angle opposite side $y$ is 30°. 2. **Formula and rules:** In a 30°-60°-90° r