📐 geometry

1. **State the problem:** We are given triangle WXY with angles $m\angle WXY = 45^\circ$, $m\angle YWX = 90^\circ$, and side $WX = 5$ feet. We need to determine which triangle (a),

1. **Problem statement:** Calculate the area of the shape consisting of a right triangle attached to a semicircle on the left. The semicircle has radius 4 meters, and the triangle

1. **State the problem:** We need to find the measure of angle $\angle FGJ$. 2. **Given information:** The angle between $FG$ and $GH$ is $57^\circ$, and the angle between $GH$ and

1. **State the problem:** We need to find the measure of angle $m\angle TQW$ given that $m\angle ZQY = 67^\circ$ and $m\angle RQX = 67^\circ$.\n\n2. **Analyze the figure:** Point $

1. **State the problem:** We have a kite DEFG with angles \(m\angle DEF = (12x - 16)^\circ\), \(m\angle EFH = (3x - 1)^\circ\), and \(m\angle DGF = 74^\circ\). We need to find \(m\

1. **State the problem:** We have a right triangle with vertices A, B, and C, where angle B is the right angle. The sides are AC = 24, BC = 10, and we want to find $\cos C$ as a fr

1. **State the problem:** We need to find the value of $\tan E$ in the right triangle $EDC$ where $ED=24$, $DC=32$, and hypotenuse $EC=40$. The right angle is at $D$. 2. **Recall t

1. **Stating the problem:** You are asked to identify and understand parts of a circle based on given points and lines: center, radius, chord, diameter, secant, tangent, point of t

1. **State the problem:** We are given two similar triangles \(\triangle ABC\) and \(\triangle PQR\) with side lengths: \(AB=6, BC=12, AC=9\) and \(PQ=10, QR=15, PR=20\).

1. **State the problem:** Raymond drew a scale drawing of a house. The garage is 4 meters wide in real life and 2 millimeters wide in the drawing. We need to find the drawing's sca

1. **State the problem:** Graph and label the points A(1, -1), B(4, 3), C(-4, 3), D(5, -2), E(-2.5, 1.5), F(2, 1.5), G(-2, -1 \frac{1}{2}), and H(1 \frac{1}{2}, -1) on the coordina

1. **State the problem:** Prove the Pythagorean Theorem using the method of arranging four right-angled triangles around a square of side length $c$. 2. **Formula and setup:** The

1. **State the problem:** We have a right triangle ABC with a right angle at C, sides AC = $2\sqrt{6}$, BC = $3\sqrt{3}$, and angle at C is 45°. We drop a height from A to BC, meet

1. **Problem Statement:** We need to find a series of transformations that map Figure R, located in the bottom-right quadrant (positive $x$, negative $y$), onto Figure S, located i

1. **State the problem:** We have two trapezoids, KLMN and K'L'M'N', where K'L'M'N' is a dilation of KLMN. We need to find the scale factor of the dilation. 2. **Recall the scale f

1. **State the problem:** We have two trapezoids, RSTU and R'S'T'U', where R'S'T'U' is a dilation of RSTU. We need to find the scale factor of the dilation. 2. **Recall the formula

1. **State the problem:** We need to find the area of a piecewise rectangular figure with given side lengths. 2. **Understand the figure:** The figure can be divided into two recta

1. **State the problem:** Find the area of a piecewise rectangular figure shaped like a large "C" with a smaller rectangle cut out from the bottom middle. 2. **Identify dimensions:

1. **State the problem:** We are given two sides of a triangle with lengths 4 inches and 7 inches, and we need to find the possible whole-number lengths of the third side. 2. **Rec

1. **State the problem:** We have two right triangles, one is a scaled copy of the other. The legs of the smaller triangle are both 15 units. The legs of the larger triangle are bo

1. **State the problem:** We have three angles $d$, $e$, and $f$ formed by three rays originating from a common point. We know one angle is $129^\circ$ and angle $d$ is a right ang