📐 geometry

1. **Problem Statement:** We have two parallel lines cut by a transversal, with some angles given: $m\angle1 = 125$, $m\angle2 = 45$, $m\angle5 = 125$. We need to find the measures

1. **State the problem:** Identify which points lie in each of the four quadrants of the coordinate plane. 2. **Recall quadrant rules:**

1. **State the problem:** A deer walks $180$ ft east, then turns $112^\circ$ clockwise and walks $105$ ft. We need to find how far the deer is from its starting point. 2. **Underst

1. **State the problem:** We are given that angle one is congruent to angle two, and we need to prove that line $l$ is parallel to line $m$. 2. **Recall the relevant theorem:** If

1. **Problem Statement:** We are given that ray $BA$ is parallel to ray $DC$ and asked to identify the type of angle pair formed by angle 1 and angle 4, and whether they are congru

1. The problem asks to identify which transformation applies to each blank: reflection or translation. 2. A **transformation** is a rule that moves or changes a figure in some way

1. **State the problem:** We need to find a series of transformations that map Figure L with vertices $(1, -7)$, $(5, -1)$, $(8, -1)$, and $(9, -6)$ onto Figure M with vertices $(-

1. **Problem Statement:** We are given a circle with a tangent line $EDC$ touching the circle at point $D$. We know the angle between the tangent $DC$ and chord $DB$ is $29^\circ$.

1. **State the problem:** We have a circle with tangent line HGF at point G. We need to find the size of angle $a$ at point G between chord $EG$ and tangent $GF$. 2. **Identify giv

1. **State the problem:** We need to find the volume of a cylinder with radius $r=4$ cm and length (height) $h=11$ cm. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** We are given that $\overline{UV} \parallel \overline{ST}$, $\overline{QR} \parallel \overline{ST}$, and $\angle 4 \cong \angle 3$. We need to prove that $

1. **Problem Statement:** We have a quadrilateral $ABCD$ with diagonal $BD$. It is given that $AB = BD$ and $BC = CD$, meaning triangles $ABD$ and $BCD$ are isosceles. The angle at

1. **Problem Statement:** We have a quadrilateral with points $A$, $B$, $C$, and $D$. The segments $AB$, $BD$, $BC$, and $CD$ are marked equal, and $\angle A = 70^\circ$. We want t

1. **State the problem:** We have two rectangular closets sharing one wall. The linen closet has an area of $12$ ft$^2$ and the clothes closet has an area of $18$ ft$^2$. We need t

1. **问题陈述**： 我们有两个三角形 $\triangle ABC$ 和 $\triangle A'B'C'$，已知 $\angle A=\angle A'$, 边 $AB=A'B'$, 边 $BC=B'C'$，要求证明这两个三角形全等。

1. **问题陈述**： 在等腰三角形 $\triangle ABC$ 中，已知 $AB=AC$，$D$ 是边 $BC$ 的中点。要求证明 $\triangle ABD \cong \triangle ACD$。

1. **Problem Statement:** You are asked to plot three sets of points on a Cartesian plane with $x$ ranging from $-18$ to $18$ and $y$ ranging from $24$ to $-24$. Then connect the p

1. **Problem Statement:** We have an equilateral triangle with a perpendicular segment of length $5$ from the left vertex to the right side, meeting it at a right angle. The upper

1. **State the problem:** We have a frustum of a cone formed by cutting a smaller cone from a larger cone. The top radius is $4$ cm, the slant height of the small removed cone is $

1. **State the problem:**\nWe need to find the surface area of a shape composed of a cylinder with height $5$ cm and a hemisphere on top with height $9$ cm. Both share the same rad

1. The problem asks if lines $m$ and $q$ are parallel. 2. To check if two lines are parallel, we find their slopes and compare.