📐 geometry

1. **State the problem:** We need to find the length of side $UV$ in rectangle $TUVW$. 2. **Recall properties of rectangles:** Opposite sides of a rectangle are equal in length. So

1. **Problem Statement:** We have a rhombus with exterior angles marked as $135^\circ$, $y$, $315^\circ$, and $45^\circ$. We need to find the size of angle $y$ and observe the rela

1. **State the problem:** We are given a triangle with sides labeled $3x + 1$, $6$, $9$, and base $33$. We need to find the value of $x$. 2. **Analyze the triangle:** The base is $

1. **State the problem:** We are given a triangle with angles $30^\circ$, $125^\circ$, and $b$, and we need to find the value of $b$. 2. **Recall the triangle angle sum rule:** The

1. **State the problem:** We have two parallel lines \(M\) and \(N\) cut by a horizontal transversal. We need to find the measure of \(\angle a\). 2. **Identify given information:*

1. **Problem Statement:** We have two semicircles each with radius $3.5$ cm, placed so that their centers are $3.5$ cm apart. We need to find:

1. **State the problem:** We need to prove that triangles $\triangle BGF$ and $\triangle FCB$ are congruent. 2. **Given information:**

1. **Problem Statement:** Calculate the circumference of a circle with radius $r = 7$ units. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **Problem:** Translate a figure 8 units left and 7 units up and find the new coordinates. 2. **Formula for translation:** If a point has coordinates $ (x, y) $, after translatio

1. **State the problem:** We need to find the sum of angles $a$, $b$, and $c$ in the given figure with intersecting lines and angles labeled $95^\circ$, $110^\circ$, $30^\circ$, an

1. **Problem 7: Find the sum of angles $a$, $b$, and $c$.** Given angles around the intersections are $95^\circ$, $110^\circ$, $30^\circ$, and $130^\circ$. Angles $a$, $b$, and $c$

1. **Problem Statement:** We have a right triangle with legs of lengths $15$ (base) and $20$ (height). Inside the triangle, a segment of length $12$ is drawn from the right angle v

1. The problem is to draw a triangle with a $90^\circ$ angle. 2. A triangle with one $90^\circ$ angle is called a right triangle.

1. The problem asks to identify the point (0,5) on a Cartesian plane. 2. A Cartesian plane consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (verti

1. Reflect P(6, -4) over the y-axis. - The reflection over the y-axis changes the x-coordinate sign: $ (x, y) \to (-x, y) $.

1. The problem is to show points on a Cartesian plane. 2. A Cartesian plane consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical).

1. Reflect point P(6, -4) over the y-axis. - The reflection rule over the y-axis is: $ (x, y) \to (-x, y) $.

1. **Stating the problem:** We have a large cone with height 45 cm and radius 9 cm. A smaller cone with height 4 cm is removed from the top, forming a frustum. We need to find the

1. **State the problem:** We are given a circle with chords intersecting inside it. The measures of arcs $FJ$ and $GH$ are $84^\circ$ and $76^\circ$ respectively. We need to find t

1. **State the problem:** We are given a circle with points S, T, U, V on the circumference and center O. The measure of arc SV is 120° and the inscribed angle at T is 82°. We need

1. **State the problem:** We need to find the bearing of point C from point B. 2. **Understanding bearings:** Bearings are measured clockwise from the north direction.