📐 geometry

1. **Problem 2.1:** Prove that when two triangles have their sides in proportion, they are equiangular. 2. **Step 1:** Suppose triangles $\triangle ABC$ and $\triangle STU$ have si

1. **Problem Statement:** Complete the table about Van Hiele levels of geometric knowledge and understanding, state differences between inductive and deductive reasoning in Geometr

1. The problem states that there are 3 triangles. 2. To analyze or solve any problem involving these triangles, we need more information such as their dimensions, angles, or relati

1. The problem is to calculate the total area of the three shapes formed on the grid. 2. The two small right triangles at the top left and top right corners each occupy a 2x2 squar

1. The problem is to calculate the total area of the composite shape formed by a right triangle and two squares arranged in a stepped pattern. 2. Identify the dimensions of each sh

1. **Stating the problem:** We need to find the volume of concrete required for a slab with thickness 7 cm (0.07 m) and the given stepped rectangular shape with dimensions as descr

1. **State the problem:** We are given the endpoints of the diameter of a circle as $(-23, 15)$ and $(1, -55)$. We need to find the equation of the circle. 2. **Find the center of

1. The problem asks to reflect a right-angled triangle with vertices A, B, and C across a diagonal line passing from bottom-left to top-right on a coordinate grid. 2. This diagonal

1. The problem asks for the coordinates of the midpoint between two points: $(-2,0)$ and $(4,4)$. 2. The midpoint formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

1. **State the problem:** We need to find the area of a circle with radius $8$ inches using $\pi = 3.14$. 2. **Recall the formula for the area of a circle:**

1. **State the problem:** We have a large rectangle made up of two smaller adjacent rectangles, both with height 8 units. The left rectangle has width 3 units, and the right rectan

1. **State the problem:** We have a large rectangle composed of two smaller rectangles side by side. The left rectangle has width $x$ and height $6$. The right rectangle has width

1. Problem 12a: Show that it is possible for 2 squares and 3 equilateral triangles to meet at one point. - Each square has an internal angle of $90^\circ$.

1. **Problem statement:** We have two figures with a circle centered at O, points C, A, B on the circumference, and a tangent line TA at A. Line COBT is straight. We need to find t

1. **State the problem:** We have a circle centered at the origin $(0,0)$ and a point on the circle at $(4,3)$. We need to find:

1. The problem asks for the perimeter of the base of a square-based pyramid. 2. The base is a square with each side measuring 6 cm.

1. Let's clarify the notation: QM, PQ, MQ, and QP represent distances or vectors between points Q, M, and P. 2. The order matters because distance or vector from point A to B is ge

1. **Problem (a): Find the size of \(\angle BAC\) to 1 decimal place.** 2. To find \(\angle BAC\), we need the coordinates or lengths of sides of triangle \(ABC\) or additional inf

1. **Problem 1: Vector triangle calculations** (a) Find the size of \(\angle BAC\) in degrees.

1. **State the problem:** We need to prove that the midpoints of the sides of any spatial quadrilateral form a parallelogram. 2. **Set up notation:** Let the vertices of the quadri

1. **Problem (a): Find the size of \(\angle BAC\) to 1 decimal place.** Since the problem does not provide explicit coordinates or side lengths, we assume \(\triangle ABC\) is give