📐 geometry

1. **State the problem:** Determine if quadrilateral $EFGH$ is congruent to quadrilateral $TUVW$ based on the given transformations and properties. 2. **Given points:**

1. **State the problem:** We have a frustum formed by cutting a smaller square-based pyramid from a larger similar pyramid. The frustum has trapezium-shaped faces all the same size

1. **State the problem:** We need to find the values of $a$ and $b$ such that the total surface area of the frustum can be expressed as $2\pi x(ax + by)$. 2. **Recall the formula f

1. **State the problem:** We need to find the values of $a$ and $b$ such that the total surface area of the frustum can be expressed as $2\pi x(ax + by)$. 2. **Recall the formula f

1. **State the problem:** We need to find the area of a parallelogram with base $16 \frac{1}{4}$ inches and height $8$ inches. 2. **Formula for area of a parallelogram:**

1. **State the problem:** We have a parallelogram with area $12$ square units. One side length is $18$ units, the other side length is $6$ units.

1. **State the problem:** We need to find the area of a parallelogram with given dimensions: base $3.5$ in. and height $6$ in. 2. **Formula for area of a parallelogram:**

1. **State the problem:** We need to find the area of a parallelogram-shaped floor where the base is $48$ ft and the height is $8$ ft less than the base. 2. **Recall the formula fo

1. **State the problem:** We need to find the area of the square poster board that is not covered by the eight identical parallelograms. 2. **Given data:**

1. **State the problem:** We need to find the total surface area of a right cylinder with height $h=8$ m and radius $r=2.5$ m, using $\pi=3.14$. 2. **Formula for total surface area

1. **Problem Statement:** We have a quadrilateral with two pairs of congruent sides (marked with tick marks) and angles $38^\circ$ and $35^\circ$ adjacent to the diagonal. We want

1. **State the problem:** We have a quadrilateral with two congruent sides and angles of $38^\circ$ and $45^\circ$ adjacent to these sides. The side opposite the $38^\circ$ angle i

1. **State the problem:** We are given a quadrilateral with points $P$, $Q$, $R$, and $S$ where $PQ \parallel RS$. We need to find the value of $y$ based on the given angle relatio

1. **State the problem:** Determine if $\triangle ABC$ is similar to $\triangle DEC$ based on the given diagram and information. 2. **Recall similarity criteria:** Triangles are si

1. **State the problem:** We need to find the area of a composite figure that looks like a trapezoid and can be decomposed into two triangles and one rectangle. 2. **Formula used:*

1. **State the problem:** We need to find the area of a trapezoid with parallel sides (bases) of lengths 3 and 10, a height of 24, and a slanted side of length 25. 2. **Formula for

1. **State the problem:** We need to find the area of a trapezoid with one pair of parallel sides (bases) measuring 6 and 8 units, and a height of 5 units. 2. **Formula for the are

1. **State the problem:** We need to find the circumference of a circle with radius $r = 10.1$ inches using $\pi$ exactly, then round the result to the tenths place. 2. **Formula:*

1. **State the problem:** We need to find the circumference of a circle with radius $r = 6.55$ cm using $\pi$ exactly, then round the result to the tenths place. 2. **Formula:** Th

1. **State the problem:** We need to find the measure of angle $m\angle I$ in rhombus $FGHI$ given that $m\angle H = u+53^\circ$ and $m\angle G = 3u-93^\circ$. 2. **Recall properti

1. **State the problem:** We are given a parallelogram $PQRS$ with $QT = b - 17$ and $ST = 2b - 54$. We need to find the value of $QT$. 2. **Important property:** In a parallelogra