📐 geometry

1. **State the problem:** We need to find the length of side $x = MN$ in a right triangle $MNO$ where the right angle is at $N$, side $NO = 7$, and angle $O = 52^\circ$. 2. **Ident

1. **State the problem:** We start with point $P(-6,1)$ and apply a series of transformations in the order given.

1. **State the problem:** Given two sides of a triangle, find which of the given options can be the length of the third side. 2. **Formula and rule:** For any triangle with sides $

1. **State the problem:** Given two side lengths of a triangle, determine which of the given options can be the third side length. 2. **Recall the triangle inequality theorem:** Fo

1. The problem asks to measure and classify triangles by their angles and sides. 2. To classify by angles:

1. **State the problem:** We have two similar rectangles D and E. Rectangle D has width 8 mm and height $x$ mm.

1. The problem involves finding the perimeter of compound shapes made up of smaller rectangles arranged in various "L" or "T" patterns. 2. The perimeter of a compound shape is the

1. **State the problem:** We need to find the exact volume of a cylinder with diameter 3 inches and height 5 inches. 2. **Formula for the volume of a cylinder:**

1. **Problem:** Find the value of $\angle BCA$ in the triangle where the side opposite $B$ is labeled $2x$. 2. **Formula and rules:** In any triangle, the sum of interior angles is

1. **State the problem:** We are given three angles with expressions in terms of $x$ and $y$: - $m\angle 5 = 2x + 3y$

1. **State the problem:** Find the area of the composite figure composed of a large rectangle with a smaller rectangle and a right triangle cut out from the bottom left. 2. **Ident

1. **State the problem:** We have two similar triangles \(\triangle ABC\) and \(\triangle XYZ\). Given sides are \(AB=5\), \(AC=7\), and unknown side \(BC=?\) in \(\triangle ABC\),

1. **Stating the problem:** We have a right-angled triangle with one angle marked as 90° and two other angles labelled as $f$ and $o$. We want to understand the relationship betwee

1. **State the problem:** We are given expressions for angles 1, 2, and 4 in terms of variables $x$ and $y$: $$m\angle 1 = 4x + 3y + 6$$

1. **State the problem:** We need to find the circumference of a circle given its diameter is 30 mm. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **State the problem:** We need to find the circumference of a circle with radius $r = 13$ m. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **State the problem:** We need to find the circumference of a circle with a diameter of 24 cm. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **State the problem:** We need to find values of $w$ and $x$ such that triangles $\triangle HIJ$ and $\triangle FEG$ are congruent. Given the sides: - $HI = x - 2w + 49$

1. **State the problem:** We need to find the perimeter of a rectangle with height $\frac{5}{8}$ ft and width $1 \frac{1}{3}$ ft. 2. **Recall the formula for the perimeter of a rec

1. The problem involves understanding the relationship between angle $b$ and the right angle in a triangle or geometric figure. 2. A vertical angle is formed when two lines interse

1. **State the problem:** We need to find the values of angles $a$, $b$, and $c$ inside a circle with given angles $39^\circ$, $50^\circ$, and a right angle $b^\circ=90^\circ$. 2.