📐 geometry

1. **State the problem:** We have two similar teddy bears. The larger bear has height 36 and width 21. The smaller bear has width 7 and height $H$. We need to find $H$. 2. **Recall

1. **State the problem:** We have a square QRPM with sides QR and PM given as expressions in terms of $x$. 2. **Recall properties of a square:** All sides of a square are equal in

1. **Problem statement:** We have an isosceles trapezoid with diagonal length $d$ and the diagonal forms an angle $\alpha$ with the longer base. We want to find the area of this tr

1. **State the problem:** We are given a triangle with angles 68°, 78°, and $x$° and need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interi

1. **State the problem:** We need to find the value of angle $x$ in a triangle where the other two angles are $60^\circ$ and $50^\circ$. 2. **Recall the triangle angle sum rule:**

1. **Stating the problem:** We need to determine which polygons among the given shapes are congruent. 2. **Recall the definition of congruent polygons:** Two polygons are congruent

1. The problem states that quadrilateral ACEG is congruent to quadrilateral MNPR. 2. Congruent quadrilaterals have corresponding sides that are equal in length.

1. **State the problem:** We are given three adjacent angles around a vertex: 56°, 26°, and $n$. We need to find the value of $n$. 2. **Formula used:** The sum of angles around a p

1. **Problem statement:** Given rectangle UVWX with diagonals intersecting at point Y, and WY = 16, find VX. 2. **Important property:** In a rectangle, the diagonals are equal in l

1. **State the problem:** We need to find the values of $x$, $y$, and $z$ in a rhombus where the angles are given as $(-x+1)^\circ$, $(3z+9)^\circ$, $108^\circ$, and $(-2y+4)^\circ

1. **Problem Statement:** Given a figure with point Q and rays QS, QR, and QT, and two angles labeled 1 and 2 at vertex Q, we need to name the sides and vertices of the angles as r

1. The problem states that a slide forms a right triangle with a length (hypotenuse) of 9 feet and a height of 8 feet. We need to find the base length. 2. We use the Pythagorean th

1. **Problem Statement:** Determine if the given parallelogram is a rhombus, rectangle, or square based on the properties of its diagonals. 2. **Key Properties of Parallelograms:**

1. The problem asks if the given parallelogram can be concluded to be a rhombus, rectangle, or square based on the given information. 2. Important properties to recall:

1. **State the problem:** Find the volume of a cylinder with height $h = 17$ ft and radius $r = 6$ ft. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** We are given a right triangle with angles $\angle A = (5x - 19)^\circ$, $\angle B = 90^\circ$ (right angle), and $\angle C = (2x + 32)^\circ$. We need to

1. **State the problem:** Find the volume of a cylinder with radius $r=2$ ft and height $h=15$ ft, rounding to the nearest tenth. 2. **Formula:** The volume $V$ of a cylinder is gi

1. **Problem Statement:** Find the volume of the solid composed of five 1-centimeter cubes arranged with four cubes in a 2 by 2 base layer and one cube stacked on top of the back r

1. **State the problem:** We need to find the volume of a solid composed of two right rectangular prisms joined together in an L-shape. 2. **Identify dimensions:** The height of bo

1. **State the problem:** We need to find the coordinates of the vertices P, Q, R, and S after reflecting them over the x-axis. 2. **Recall the reflection rule:** Reflecting a poin

1. **State the problem:** We have two triangles sharing a side. The left triangle is a right triangle with one angle of 65° and the right triangle has angles 50°, 80°, and an unkno