📐 geometry

1. **State the problem:** Find the exact length of the midsegment of trapezoid $STUV$ with vertices $S(-2,4)$, $T(-2,-4)$, $U(3,-2)$, and $V(13,10)$. 2. **Recall the midsegment for

1. **State the problem:** We need to find the surface area of a hemispherical dome with radius $r = 6$ cm. 2. **Formula for surface area of a hemisphere:** The surface area of a he

1. **Problem statement:** We have an isosceles triangle with two equal sides of 5 cm and a base of 6 cm (divided into two segments of 3 cm each). A perpendicular height from the ba

1. **Problem Statement:** Given a quadrilateral with vertices A, B, C, and D, where segment AC is congruent to segment AD, and segment CD is congruent to segment BD, we want to ana

1. **State the problem:** We need to find the approximate radius $r$ of a sphere given its volume $V = 38808$ cubic inches. 2. **Formula:** The radius $r$ is approximated by the fo

1. **Problem statement:** Find the volume of a solid consisting of a cone with a half-sphere on top. The radius of both the cone and the half-sphere is 10 cm, and the height of the

1. **State the problem:** Calculate the area of a rectangle with base length $29.5$ m and height length $18.96$ m. 2. **Formula:** The area $A$ of a rectangle is given by the formu

1. **State the problem:** Find the angle $C$ in a triangle with sides $AC=12$, $CB=10$, and $AB=9$. 2. **Formula used:** Use the Law of Cosines to find angle $C$:

1. **State the problem:** We need to find the length of side AC (denoted as $x$) in triangle ABC where \(\angle A = 80^\circ\), \(\angle B = 55^\circ\), and side BC = 3.8 cm. 2. **

1. **State the problem:** We need to find the total area of the rectangular faces of the 3D shape. The given dimensions are 7 cm and 8 cm for the edges of one rectangular face. 2.

1. **Problem statement:** We have a triangular prism with a base triangle of base length 7 cm and a prism length (height) of 8 cm. The shaded face is a rectangular side face of the

1. The problem asks for the coordinate location of Cindy's house, which is halfway between Gabe's house and the library on the first graph. 2. To find the midpoint between two poin

1. **Problem 3:** Gabe walks from his house to the library, then to the gymnasium. We need to find the total distance he walked. 2. **Identify coordinates:** From the description a

1. **Problem:** Determine if the two triangles are congruent using ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria. 2. **Recall the criteria:**

1. The problem asks to identify the coordinates of a point from the given options on the first graph. 2. The first graph shows two circles: a smaller circle centered at (0,2) with

1. **State the problem:** We are given points $(x,y)$ as $(0,-3)$, $(-2,1)$, and $(1,2)$ and a graph with two shaded circles. We need to analyze or solve based on this data. 2. **I

1. The problem involves understanding the property of angles in the same segment of a circle. 2. The property states: "Angles subtended by the same chord in the same segment of a c

1. **Problem statement:** We are given a circle with center O and points A, B, C, D, E, F on the circumference. We know the central angle $\angle AOB = 110^\circ$ and an inscribed

1. **State the problem:** We need to find the length of segment $AB$ in the given geometric figure. 2. **Analyze the figure:** The figure has two right angles at the bottom corners

1. **بیان مسئله:** الف) عکس قضیه: اگر در یک مثلث زاویه های روبه رو به دو ضلع با هم برابر باشند، آنگاه آن دو ضلع با هم برابرند.

1. مسئله اول: رسم مثلث متساوی الساقین با راس A و قاعده روی خط d که فاصله A تا d برابر ۴ سانتی‌متر و طول ساق‌ها ۶ سانتی‌متر است. 2. برای رسم مثلث متساوی الساقین با قاعده روی خط d و