📐 geometry

1. **State the problem:** We need to find the area of a triangle with all sides measuring 4 cm. 2. **Identify the type of triangle:** Since all sides are equal (4 cm), this is an e

1. **State the problem:** We need to find the central angle $x$ in a circle given an inscribed angle of $70^\circ$ that subtends the same arc. 2. **Recall the rule:** The central a

1. **Problem Statement:** Identify a pair of alternate exterior angles, a pair of corresponding angles, and a pair of alternate interior angles formed by two parallel lines $m$ and

1. **State the problem:** We have a cylindrical water bottle with height $15$ cm and inner radius $4$ cm. The water height is currently $8$ cm, and the bottle will be full (height

1. **Problem Statement:** Given a line segment $\overline{CD}$, construct its perpendicular bisector and label the intersection point as $E$.

1. **Problem Statement:** Describe the reflections and/or rotations that carry a square onto itself. 2. **Understanding the square's symmetry:** A square has several symmetries inc

1. **State the problem:** We have triangle EGD with point F on segment EG such that EF = $x$ and FG = $x + 10$. We know ED = 24 and GD = 54. We want to find the length EF. 2. **Ide

1. **Stating the problem:** We are given two triangles, one acute with one angle marked and one side marked with a single tick, and the other a right triangle with the vertical leg

1. **Problem statement:** We have an isosceles triangle $\triangle ABC$ with $AB = CB$, area $= 30$ cm$^2$, and base $AC = 12$ cm. We need to find the measure of $\angle ABC$ to th

1. **State the problem:** We are given two angles expressed in terms of $x$: $4x - 1$ degrees and $2x + 5$ degrees, and we need to find the measure of angle $m\angle MYW$. The diag

1. **State the problem:** We are given two angles at point Y, one measuring $(4x - 1)^\circ$ and the other $(2x + 5)^\circ$, and these angles are adjacent and form a right angle (9

1. **State the problem:** We have a right triangle with vertices K, L, and J, and a perpendicular segment KM from K to LJ. Given lengths are $KM=6$ and $MJ=8$. We need to find the

1. **Stating the problem:** We are given a geometry problem involving inequalities (inequations). We need to analyze the geometric conditions and solve the inequalities accordingly

1. **State the problem:** Annabel wants to know how much wood flooring she needs for her bedroom and closet. We need to find the total area of both rooms.

1. **State the problem:** We have two right triangles sharing a vertex, with the larger triangle having hypotenuse $w$ and base $x$, and the smaller triangle inside it having legs

1. **Problem Statement:** Determine the coordinates $(x_i, y_i)$ for $i=1$ to $5$ of five points equally spaced by angle on a quarter circle centered at the origin with radius 1, l

1. **State the problem:** We have a triangle with sides labeled 15, 12, and 10, and two horizontal segments inside it labeled $y$ and 4 on the upper segment, and $x$ on the lower s

1. **State the problem:** We have a large triangle with a base of 13 and two segments inside parallel to the base, creating smaller triangles with sides labeled 4, 6, 2, 6, 9, and

1. **State the problem:** We are given a circle with points O, M, P, N on the circumference and Q as the center. Angles at O and P are 62° and 94° respectively. We need to solve fo

1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°, and the hypotenuse is given as $7\sqrt{3}$ meters. We need to find the length $j$ of the side oppo

1. **State the problem:** We need to find the length $x = VU$ in the right triangle $\triangle VUT$ where $\angle U = 90^\circ$, $UT = 64$, and $\angle UTV = 70^\circ$. 2. **Identi