📐 geometry

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

1. **State the problem:** We have four rays originating from a point forming angles around it. Given one angle is 33° and a right angle of 90°, we need to find the missing angles $

1. **State the problem:** We are given a right-angled triangle ABC with right angle at B, sides AB = 4 m, BC = 6 m, and point D on BC such that BD = 1 m and DC = 5 m. We need to us

1. The problem asks to construct the three perpendicular bisectors of each triangle and show they are concurrent, meaning they intersect at a single point called the circumcenter.

1. The problem is to identify the missing view marked with a "?" from a set of options labeled A to L. 2. The missing view should logically correspond to the combination or transfo

1. **Stating the problem:** We need to find the measures of angles $\angle G$, $\angle H$, and $\angle I$ in triangle $GHI$. 2. **Given information:** There is an angle of $110^\ci

1. **State the problem:** We are given a triangle with two known angles, $110^\circ$ and $20^\circ$, and we need to find the measure of the third angle. 2. **Formula used:** The su

1. **Problem Statement:** Solve for $x$ in the conjoined triangles $QRU$ and $TSU$ where both have an angle of $54^\circ$ and share side $TU$.