📐 geometry

1. **State the problem:** We are given a triangle with angles $C = 33^\circ$ and $B = 70^\circ$. We need to find the measure of angle $A$. 2. **Recall the triangle angle sum rule:*

1. **Problem Statement:** Given a quadrilateral $ABCD$ where $E$ is the midpoint of both $AD$ and $BC$, prove that the line segments $AB$ and $CD$ are parallel.

1. **State the problem:** Given $AP \perp AB$, $BQ \perp AB$, and $AP \cong BQ$, prove that $O$ is the midpoint of both $AB$ and $PQ$.

1. **Problem Statement:** We need to find the size of angle $XYZ$ in a right triangle $XYZ$ where the right angle is at $X$. The side $ZX$ (vertical) is $12$ cm and side $XY$ (hori

1. **State the problem:** We need to find which equation can be used to find the missing angle $q$ in a triangle with angles $29^\circ$, $45^\circ$, and $q^\circ$. 2. **Recall the

1. **State the problem:** We need to find the volume of an irregular stepped rectangular prism with given dimensions. 2. **Understand the shape:** The solid can be divided into two

1. **Problem Statement:** We are given a rhombus $ABCD$ with side length $15$ cm and a segment $EC = 12$ cm. We need to find the area of the right triangle $BEC$.

1. **Problem Statement:** Given that $\overline{NL} \parallel \overline{QO}$ and $\overline{MN} \parallel \overline{PQ}$, prove that $\triangle LMN \sim \triangle OPQ$.

1. **Problem Statement:** We are given a triangle with vertices at $(-6,4)$, $(-5,2)$, and $(-1,2)$.

1. **Problem Statement:** We are given that segment $CT$ bisects angle $SCA$ and that angle $S$ is congruent to angle $A$. We need to prove that triangle $SCA$ is isosceles with $S

1. **State the problem:** We need to prove that triangle $SCA$ is isosceles, meaning $SC \cong CA$, given that segment $CT$ bisects angle $SCA$ and angle $S \cong$ angle $A$. 2. **

1. **State the problem:** We need to find the measure of angle $\angle Z$ in a diamond-shaped quadrilateral $WZ YX$ with given angle expressions. 2. **Recall properties:** A diamon

1. **Problem Statement:** Calculate the slant height of a pyramid to the nearest tenth. 2. **Understanding the Slant Height:** The slant height ($l$) of a pyramid is the distance f

1. **Problem Statement:** We have a right square pyramid with a surface area of $50.75$ square inches and a base length of $3.5$ inches.

1. **State the problem:** We need to find the surface area of a square pyramid with a base side length of $45$ inches and a slant height of $50$ inches. 2. **Formula for surface ar

1. **State the problem:** We need to determine if the Mad Hatter robot, which is 17.75 inches tall, fits inside a plexi-glass box with given dimensions and surface area constraints

1. **State the problem:** We need to find the measure of $\angle HKJ$ given two expressions for angles related to points $J$ and $K$ on parallel lines cut by a transversal. 2. **Id

1. **Problem Statement:** Determine if the Mad Hatter robot meets the height requirement to fit inside a plexi-glass box with given dimensions and surface area. 2. **Given:**

1. **State the problem:** We need to find the perimeter of an L-shaped polygon with given side lengths in feet. 2. **Identify the known sides:** The polygon has sides of lengths $8

1. **Problem Statement:** We have three solid shapes: a cube, a cone, and a cylinder.

1. **Problem Statement:** We need to find the percentage of the area of the segment ACB cut off by the straight line AC relative to the remaining area of the sector AOC.