📐 geometry

1. **Problem statement:** Given two parallel lines $a \parallel b$ and a transversal, with an angle of $120^\circ$ at the upper intersection and expressions $7x - 10$ and $10y - 10

1. **Problem Statement:** Determine whether the triangles in problem 9 are similar by AA~, SSS~, SAS~, or not similar. 2. **Given:** Two triangles connected by segment UW with angl

1. **State the problem:** Find the surface area of the composite L-shaped figure made of two rectangular prisms joined perpendicularly. 2. **Identify dimensions:**

1. **State the problem:** Find the volume of the composite figure composed of two rectangular prisms joined together. 2. **Identify dimensions:**

1. Problem: If J is the circumcenter of \(\triangle DEF\), find the length of \(DH\). Given segments: \(EG = 8x - 17\), \(GF = 6x - 7\), and \(JH = 8\). 2. Since \(J\) is the circu

1. **State the problem:** We have two right triangles, ABC and ACD, with given angles and some side lengths. We need to find the missing sides $k$, $m$, $x$, and $y$. 2. **Triangle

1. **Problem:** Find the perimeter of a kite with sides 12 and 20. 2. **Formula:** Perimeter of a kite = 2 × (sum of lengths of two distinct adjacent sides).

1. **State the problem:** We are asked to find the measure of angle $\angle F$ in the circle with center $O$, given $m\angle DOE = 72^\circ$ and $m\angle EOG = 84^\circ$, and $EF$

1. **State the problem:** We are given angles formed by rotating vectors \(\overrightarrow{AB}\) and \(\overrightarrow{CD}\) to create angles \(\angle XPA\) and \(\angle XPC\) with

1. **State the problem:** We are given that $m\angle WXZ = 95^\circ$ and $m\angle 1$ is 27° more than $m\angle 2$. We need to find $m\angle 2$. 2. **Understand the angles:** $\angl

1. **Problem Statement:** Given three sets of parallel lines: $a \parallel b$, $c \parallel d$, and $e \parallel f$, and the segments with lengths 12, 5, and 8, find the missing si

1. **Problem Statement:** Draw the preimage and image of triangle PQR under a translation along the vector $\langle -1, 3 \rangle$. The triangle vertices are $P(1, -3)$, $Q(3, -1)$

1. **Problem Statement:** Translate quadrilateral ABCD along the vector \(\langle -4, -6 \rangle\).

1. **Convert the vector \(\langle -3,1 \rangle\) into coordinate notation:** The vector is already in coordinate notation as \(\langle x,y \rangle\). So the coordinate notation is

1. **Convert the vector <-3, 1> into coordinate notation.** The vector is already in coordinate notation as $\langle -3, 1 \rangle$.

1. **Problem statement:** Given a circle with center $O$, two tangent segments $FI$ and $FG$ touch the circle at points $I$ and $G$ respectively. The segment $IG$ passes through th

1. **State the problem:** We have a rectangle WXYZ with diagonals intersecting at point P. Given that $WP = 4x + 6$ and $PY = 26$, find the value of $x$. 2. **Recall properties of

1. **Problem statement:** Given parallelogram ABCD with angles at A as $6x$, at B as $72^\circ$, and at D as $72^\circ$, find the value of $x$. 2. **Recall properties of parallelog

1. **State the problem:** Terry made a plastic birdhouse shaped like a rectangular prism with dimensions 10 inches (length), 6 inches (height), and 8 inches (width). We need to fin

1. **Problem Statement:** We have a triangle with vertices at points $P(2, -1)$, $Q(2, -3)$, and $R(4, -3)$. We want to find the image of this triangle after a translation along th

1. The problem asks to identify the correct net for a rectangular prism. 2. A rectangular prism has 6 faces: 3 pairs of rectangles, each pair with the same dimensions.