📐 geometry

1. **State the problem:** Identify which shapes are translations of shape X. A translation means the shape is shifted without rotation or resizing. 2. **Recall the vertices of shap

1. The problem asks to identify which shapes are translations of shape X. 2. A translation means the shape has the same size and orientation but is shifted to a different position

1. The problem asks: Do equal arcs subtend equal angles at the circumference of a circle? 2. Important concept: In a circle, an arc is a portion of the circumference. The angle sub

1. **הבעיה:** נתון מקבילית ABCD עם נקודה E על הצלע AB. הישרים CE ו-DE חוצים את הזוויות BCD ו-ADC בהתאמה.

1. **State the problem:** We are given a diagram with angles 27° and 112° and need to find the angle $x$ formed between lines $OC$ and $OP$. 2. **Identify relationships:** The poin

1. Let's clarify how to find angles in a triangle or any geometric figure. 2. Typically, angles are found using rules like the Triangle Sum Theorem, which states that the sum of an

1. **Stating the problem:** Construct a triangle where one angle $m$ is less than 45 degrees, another angle $m$ is less than 90 degrees, and one side length is 3.6 cm. 2. **Underst

1. **Problem statement:** Establish the correspondence between angles $\alpha$ and $\beta$ in a parallelogram. 2. **Recall the property:** In a parallelogram, adjacent angles are s

1. **State the problem:** We have 6 tiles each of size 1cm² and want to find what fraction of a right-angled triangle with legs 3cm and 4cm these tiles will cover. 2. **Formula for

1. **State the problem:** Given triangles \(\triangle ART \sim \triangle FIN\) with altitudes \(AS = 4\) and \(FE = 3\), and sides \(AT = x+1\) and \(FN = x-1\), find the lengths o

1. **State the problem:** We have parallelogram KLMN with sides LM = 5 cm, MN = 3 cm, and diagonal LN = 3.2 cm. We need to find the measure of angle LKN to the nearest degree (Part

1. Problem a: Find $x$ where vertical angles are equal and adjacent angles sum to 180°. 2. Use the rule: adjacent angles on a straight line sum to 180°.

1. **Problem statement:** Calculate the missing angle in each diagram where all angles at a point add up to 360°. 2. **Formula:** Sum of angles at a point = 360°.

1. The problem involves understanding the transformation of a point on a figure in the coordinate plane. 2. We are given an original point $(3, 5)$ and its image after transformati

1. **State the problem:** We need to find which arcs have the same size central angle given their arc lengths and radii. 2. **Formula:** The central angle $\theta$ (in radians) for

1. The problem asks for the radian measure of angle \(\angle A\) in a circle with radius 3, where the angle is marked as \(\pi\) radians. 2. The radian measure of an angle in a cir

1. **State the problem:** Calculate the surface area of a gas tank composed of a cylinder with a hemisphere on each end.

1. **State the problem:** We need to find the surface area of a shape made by joining a hemisphere on top of a cylinder. The hemisphere and cylinder share the same radius $r=9$ cm,

1. **State the problem:** Find the distance between the points (7, 9) and (2, -3) using the right triangle formed by these points and the point (2, 9). 2. **Formula used:** The dis

1. The problem is to find the angle $\angle AOB$, not $\angle ACB$.\n\n2. To find $\angle AOB$, we need to understand the points $A$, $O$, and $B$ and their positions or vectors. U

1. **Problem statement:** We have two towers represented by two circles with radii 100 km and 150 km. A common external tangent line CE touches the circles at points C and E. We wa