📐 geometry

1. **Problem statement:** Find the unknown angle $x$ in the given figure with two tangent circles and given angles $37^\circ$, $60^\circ$, and $80^\circ$. 2. **Understanding the fi

1. The problem is to determine which angle is congruent to \(\angle HUI\) from the given options: \(\angle GUI\), \(\angle IGU\), or \(\angle UIG\). 2. Congruent angles have the sa

1. The problem asks which pair of congruent corresponding parts is needed to prove that two triangles are congruent using the SAA (Side-Angle-Angle) congruence conjecture. 2. The S

1. **Stating the problem:** We are given six expressions involving variables $d$ and $b$:

1. **State the problem:** We have a swimming pool with an inside perimeter of 24 meters and an outside perimeter of 48 meters. We want to find how many stepping stones are needed t

1. **State the problem:** We are given triangle $\triangle ABC$ with sides $AB=0.9$, $BC=1$, and $AC=1.5$. We need to determine which of the given triangles $\triangle DEF$ or $\tr

1. **Stating the problem:** We are given a segment \(\overline{BD} = 12\) cm and points \(A, B, C, D, O\) on a figure. We need to find the length \(\overline{BO}\). 2. **Understand

1. **Problem statement:** Find the area of the shaded quarter circle inside a square with side length 7 cm. 2. **Formula used:** The area of a quarter circle is given by

1. **State the problem:** We need to find the perimeter of the blue shape drawn on a 7 by 7 grid where each square side measures 1 cm. 2. **Understand the perimeter:** The perimete

1. **State the problem:** We need to find the perimeter of an L-shaped figure drawn on a 6x6 grid where each square side is 1 cm. 2. **Understand the shape:** The L-shape covers 3

1. **State the problem:** Given parallelogram ABCD with diagonals AC and BD perpendicular ($AC \perp BD$), prove that $AB \cong BC$. 2. **Recall properties:** In a parallelogram, d

1. **Problem:** Given a right-angled triangle PQR with right angle at R, hypotenuse PQ = 16 cm, and leg PR = 8 cm, find the length of QR to 2 decimal places. 2. **Formula:** Use Py

1. **State the problem:** Find the length of the radius of the circle given the chords and radii in the diagram.

1. **Stating the problem:** We have a vertical figure composed of a rectangle with length $3m\ 5cm$ connected on top to an ellipse with height $85cm$ and on the bottom to another e

1. The problem is to find the area of a shape with given side lengths 2 m, 5 m, and 4 m. 2. Since the problem does not specify the shape, we assume it is a triangle with sides 2 m,

1. **Problem statement:** Find the coordinates of point $X$ on the line segment $\overline{RS}$ such that $X$ is $\frac{1}{6}$ of the distance from $R$ to $S$. 2. **Given:**

1. **Problem statement:** Find the coordinates of point X on line segment AB such that X is \(\frac{1}{5}\) of the distance from A to B. 2. **Formula:** To find a point dividing a

1. The problem is to find the formula for the area of a parallelogram. 2. The area $A$ of a parallelogram can be calculated using the formula:

1. **State the problem:** We need to determine if the new TV screen (16 inches wide and 9 inches high) is a dilation of the old TV screen (20 inches wide and 15 inches high). 2. **

1. The problem asks for the complement of the angle $90 - x$ degrees. 2. Recall that the complement of an angle $\theta$ is $90^\circ - \theta$.

1. The problem asks for the complement of an angle measured in degrees, denoted as $a$. 2. The complement of an angle is defined as the amount by which the angle must increase to r