📐 geometry

1. **Problem Statement:** We are examining the reflexive property in geometry, which states that a segment or angle is equal to itself, often written as $AB = BA$. 2. **Context:**

1. **State the problem:** We have two mathematically similar shapes. The smaller shape has an area of 52.5 cm² and a side length of $m$ cm. The larger shape has an area of 134.4 cm

1. **State the problem:** We have a circle with center O and radius $r$ cm. Points A and B lie on the circumference, and the central angle $\angle AOB$ is 140°. The area of the sha

1. **State the problem:** We are given a trapezium with two angles on the left side: the top-left angle is $97 - 3x$ degrees and the bottom-left angle is $69 + 5x$ degrees. We need

1. **State the problem:** We are given a trapezium with two angles on the left side: the top left angle is $97 - 3x$ degrees and the bottom left angle is $69 + 5x$ degrees. We need

1. The problem asks for the name of a quadrilateral with rotational symmetry of order 2 and no lines of symmetry. 2. Rotational symmetry of order 2 means the shape looks the same a

1. The problem asks to identify quadrilaterals based on their symmetry properties. 2. (a) A quadrilateral with rotational symmetry of order 2 but no lines of symmetry is called a *

1. **Stating the problem:** We need to find the volume of the frustum of a pyramid OABCD, where the height of the frustum is 16 cm, and the base and top areas are related to the gi

1. **State the problem:** We need to find the volume of the frustum of a pyramid OABCD with height 16 cm, given the base edges and the formula for the volume of a pyramid $V = \fra

1. **Stating the problem:** We have two lines $l_1$ and $l_2$ intersected by a transversal $t$. We need to:

1. **State the problem:** We need to find the value of $x$ that makes triangles $\triangle ONM$ and $\triangle SRQ$ similar by the SAS (Side-Angle-Side) similarity theorem. 2. **Re

1. The problem asks to identify the missing statements in steps 3 and 4 to prove that triangles ABC and ZYX are similar using the given information. 2. Given:

1. **State the problem:** We are given two triangles, \(\triangle ABE\) and \(\triangle ACD\), and told they are similar by the SAS similarity theorem. We know \(AB=6\), \(BC=30\),

1. **State the problem:** Determine if triangles △LMN and △PQR are similar, congruent, or neither using side lengths. 2. **Given side lengths:**

1. **Problem Statement:** We are given two triangles △LMN and △XYZ with some side lengths known. We want to prove that △LMN ~ △XYZ by the SSS (Side-Side-Side) similarity theorem. 2

1. **State the problem:** We need to find the shortest distance from point Q to the line segment PR in triangle PQR. 2. **Given data:**

1. **Problem Statement:** We have two right-angled triangles joined by a common side. One triangle has an angle of 60° and a vertical side labeled $n$. The other triangle has angle

1. **State the problem:** Calculate the volume of a square-based pyramid with base dimensions 23 cm by 16 cm and a slant height of 34 cm. 2. **Formula for volume of a pyramid:**

1. **Problem Statement:** (a) Explain the difference between capacity and volume to Grade 6 pupils.

1. **Problem Statement:** (a) Explain the difference between capacity and volume to Grade 6 pupils.

1. **Problem Statement:** Given two parallel lines $O$ and $m$ cut by a transversal $k$, find the values of angles $z$ and $x$ where the angles are $(3x + 15)^\circ$, $z^\circ$, an