📐 geometry

1. **State the problem:** We need to find the size of angle $x$ in a figure with intersecting lines and given angles $65^\circ$ and $137^\circ$. 2. **Identify angle facts used:**

1. We will list the main geometric formulas involving the trigonometric functions sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). 2. **B

1. **State the problem:** We have a small unshaded rectangle measuring 2 cm by 1 cm. Two copies of this rectangle are joined side by side horizontally to form a larger shaded recta

1. **State the problem:** We are given a triangle with angles labeled as $3x$, $2x$, and $x + 30$. We need to find the size of the largest angle. 2. **Recall the rule:** The sum of

1. **State the problem:** We have a composite shape made of a triangle on top of a trapezium. The area of the triangle is given as 28 cm². The triangle's height is 7 cm, and the tr

1. **Problem statement:** We have a square-based pyramid ABCDE with volume 180 cm³. M is the center of the base ABCD and lies vertically below E. Given $\vec{EM} = 7.5$ cm, find:

1. **State the problem:** We need to find the total area enclosed by two triangles joined at a vertex, sharing a side. The left triangle has a side length of 5 cm and an included a

1. The problem asks to find the size of angle AED and the value of x in a circle with points A, B, D, E on the circumference and point C outside. 2. Since AE = AD, triangle AED is

1. **State the problem:** We need to find the size of angle $EFG$ in a cyclic quadrilateral $EFGD$ inscribed in a circle, given that angle $D$ is $62^\circ$ and angle $EFG$ is $118

1. **State the problem:** Calculate the area of the cross section of the slide, which is a right triangle with a stepped platform inside. 2. **Identify the dimensions:**

1. **Problem statement:** We have a right-angled triangle ABC with right angle at B. AB = 18 cm (vertical side), BC = 6 cm (horizontal side).

1. The problem asks if a right triangle can be solved given only the measures of its two acute angles and no side lengths. 2. In a right triangle, the sum of the three angles is al

1. **State the problem:** Find the surface area of a rectangular prism with dimensions 2 3 inches, 4 6 inches, and 2 8 inches. 2. **Interpret the dimensions:** The dimensions given

1. **State the problem:** We have a right triangle with legs of lengths 2 cm and $x$ cm, and a hypotenuse of 10 cm. We need to find the perimeter of the triangle. 2. **Use the Pyth

1. **Reflect the pre-image over the x-axis.** The reflection rule over the x-axis is given by:

1. **Énoncé du problème :** On considère la figure avec les points A, B, C alignés, les triangles ABE et EBD rectangles respectivement en A et B.

1. The user message is incomplete and does not specify a full problem or question. 2. To assist effectively, please provide the complete coordinates or the full problem statement.

1. **Problem statement:** A triangle's height is 1 cm longer than its base, and its area is 21 cm². Find the height.

1. **Problem statement:** Find the unknown sides in the similar triangles from the first diagram, starting with TV. 2. **Step 1: Understand the problem and given data.**

1. **State the problem:** We are given two angles at point O, one measuring $7x$ and the other $8x$, and the angle between these two rays is $60^\circ$. We need to find the value o

1. The problem asks to find the correct translation rule that maps triangle BCD to triangle B'C'D'. 2. A translation rule moves every point $(x, y)$ to a new point $(x + a, y + b)$