📐 geometry

1. The problem asks which sets of three lengths can form a right triangle. 2. To determine if three lengths $a$, $b$, and $c$ form a right triangle, we use the Pythagorean theorem:

1. **State the problem:** We need to find the values of $w$, $x$, and $y$ in a parallelogram where the sides are labeled as follows: - Side AB: $x + 16$

1. **Problem statement:** Given kite RSTU with angles labeled as $m\angle R = x + 30^\circ$, $m\angle T = x^\circ$, and $m\angle U = 125^\circ$, and sides RS = RU and ST = UT, find

1. The problem asks about the properties of an equilateral triangle, specifically the relationship between its sides. 2. An equilateral triangle is defined as a triangle where all

1. **Stating the problem:** We are given a triangle CEB with sides DE = 80 m, EC = 41 m, angle CEB = 37°, AE = 0 m, and EB = 9 m. We need to find (i) the length BC using the Pythag

1. **State the problem:** We have a triangle with angles 73° and 33°, and sides opposite these angles labeled as $2x - 1$ and $x$ respectively. We need to find the value of $x$ to

1. **State the problem:** We need to find the length of segment $BM$ in a circle where two chords $ML$ and $JK$ intersect at point $B$ inside the circle. 2. **Recall the chord inte

1. **Problem statement:** Given that $CD=4$ and the perimeter of triangle $ABC$ is 23, find the perimeter of triangle $ABE$. 2. **Understanding the problem:** We have triangle $ABC

1. **Problem statement:** Given $m \angle YXW = 21^\circ$, $YW = 5$, and $WZ = 5$, find $m \angle ZXY$ in triangle $XYZ$ with right angles at $W$. 2. **Understanding the problem:**

1. **State the problem:** We need to find the length of side $x = BC$ in quadrilateral $ABCD$ given angles and side lengths. 2. **Given data:**

1. **Problem statement:** Find the length of side $x = BC$ in the quadrilateral with given sides and angles. 2. **Given:**

1. **State the problem:** We are given a trapezoid with the top base labeled as $3x + 2$, the middle segment inside the trapezoid labeled $17.5$, and the bottom base labeled $21$.

1. **State the problem:** We have a trapezoid with the top base length 10, the middle segment length 12, and the bottom base length 2x. The trapezoid has two pairs of congruent leg

1. **Problem Statement:** Given a rectangle CMXZ, determine whether each of the following statements is always, sometimes, or never true:

1. The problem asks to redraw a rectangle originally drawn with a scale of 1 unit = 2 ft using a new scale of 1 unit = 4 ft. 2. The original rectangle has dimensions 2 ft by 4 ft.

1. **State the problem:** We need to find the shaded area of an annulus, which is the region between two concentric circles with radii 6.5 cm and 2.3 cm. 2. **Formula:** The area o

1. **Problem statement:** We are given a right triangle where \( \tan \theta = 0.75 \) and the lengths of the two sides adjacent to the right angle are single-digit whole numbers.

1. **Problem statement:** We have a triangle ABC with incentro I, area 12 cm², and perimeter 18 cm. A circle centered at I is tangent to side BC at point D.

1. **State the problem:** We are given the surface area of a shape labeled as $b$ and it is expressed as $(22y + 60)$ cm$^2$. 2. **Understanding surface area:** Surface area is the

1. **State the problem:** We have a cube A with edge length $x$ cm and volume 216 cm³. We need to find the value of $x$. 2. **Formula for volume of a cube:** The volume $V$ of a cu

1. The problem involves analyzing the angles in a kite-shaped figure with given angle labels and some known angle measures: 42°, 30°, and 30°. 2. In a kite, two pairs of adjacent s