📐 geometry

1. The problem asks to identify which sets of three side lengths form a right triangle. 2. Recall the Pythagorean theorem: for a right triangle with sides $a$, $b$, and hypotenuse

1. **Problem statement:** We have two circles E and F with a common tangent line AC touching circle E at C and circle F at B. Given lengths DE = 15 and FB = 7, we need to find the

1. **State the problem:** Find the distance between points $C(-9, 2)$ and $D(-7, 5)$ on the Cartesian plane. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ a

1. **State the problem:** Find the missing height $h$ of a triangular prism given the surface area and dimensions of the base.

1. **Problem statement:** Find the measure of angle 2 ($m\angle 2$) in the rhombus WUTV where angles at vertices V and W are each 28°. 2. **Properties of a rhombus:**

1. **Stating the problem:** We are given a rectangle and two triangles with areas 8 square meters, 4 square meters, and 4 square meters respectively. We need to find the total area

1. The problem involves finding the area of a driveway represented on a grid where each small square is 1 meter by 1 meter. 2. The driveway is composed of one large rectangle and t

1. The problem asks to draw the side elevation of a 3D stepped rectangular block starting from the point marked with a green dot at the bottom front corner of the base prism. 2. Th

1. **State the problem:** We need to find the area of triangle ABC where the right angle is at vertex A. 2. **Identify the sides:** Given that AB is vertical with length $\sqrt{3}$

1. The problem states that the sum of the angles in a triangle is 180 degrees. 2. The angles given are $32c + 5$, $24c$, and $c + 32$ degrees.

1. **Problem statement:** Find the length of diagonal $BE$ in cuboid $ABCDEFGH$ with dimensions $AB=11$ cm, $AD=6.1$ cm, and $AE=4.2$ cm. 2. **Formula:** The length of a space diag

1. The problem asks to name the angle pairs formed by two parallel lines cut by a transversal and to type the 4-letter code in ALL CAPS with no spaces. 2. Important angle pair type

1. **State the problem:** We need to find the surface area of a right circular cylinder with height $h=19$ in and diameter $d=13$ in, using $\pi=3.14$.

1. **State the problem:** Find the surface area of a right circular cone with height $19$ cm and base radius $3$ cm, using $\pi = 3.14$. 2. **Formula for surface area of a cone:**

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula:** The standard form of a circle's equation with center $(h,

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula:** The standard form of a circle's equation with center $(h,

1. The problem asks to measure the angles of four polygons: two triangles (a-b-c and d-e-f) and two quadrilaterals (g-h-i-k and m-n-o-p) using a protractor, and then to draw and me

1. **State the problem:** Calculate the surface area of a triangular prism with triangular base sides 4 in, 5 in, and 6 in, and height (length) 3 in.

1. **State the problem:** We have a rectangle with length 32 cm and width 14 cm. Two semicircles, each with diameter 14 cm, are cut out from the shorter sides. We need to find the

1. **State the problem:** We have a rectangular paperboard measuring 27 inches long and 22 inches wide. A semicircle with diameter equal to the width (22 inches) is cut out from th

1. **State the problem:** We have two triangles, △ABC and △DEF, with given sides and angles: $AB=15$, $BC=20$, $\angle B=37^\circ$, $DE=24$, and $\angle E=37^\circ$. We want to fin