📐 geometry

1. The problem asks to identify the theorem, term, or corollary represented by the congruence of triangles \(\triangle ABC \cong \triangle DEF\) and the markings shown. 2. Given \(

1. **State the problem:** We need to find the surface area of a triangular prism with triangular base sides 13 cm, 16 cm, and 12 cm, and prism length (depth) 5 cm. 2. **Calculate t

1. **State the problem:** Find the lengths of the line segments \(\overline{CM}\) and \(\overline{AB}\) using the distance formula. 2. **Calculate \(CM\):**

1. **State the problem:** Prove that right triangles $\triangle ABD$ and $\triangle CBD$ are congruent. 2. **Find the length of segment $AD$ using the distance formula:**

1. **State the problem:** We are given right triangles \(\triangle ABD\) and \(\triangle CBD\) with points \(A(0,0)\), \(B(4,6)\), \(C(8,0)\), and \(D(4,0)\). We need to prove that

1. Let's first clarify the problem: we want to find the angle $\angle ABO$ in a given geometric figure where points A, B, and O are defined. 2. Typically, to find an angle like $\a

Problem: Find the mass of a cylindrical cake with radius 5.5 cm and height 11 cm, given that each cubic centimetre has mass 0.4 g, and give the final answer to 1 d.p. 1. The volume

1. **Stating the problem:** We have a shape composed of an ellipse and two straight parallel lines connecting semicircles at each end. The total length of the shape is 250 meters,

1. The problem asks how many complete cylinders can be made from a given material or volume. 2. To solve this, we need to know the total volume or material available and the volume

1. **State the problem:** We have a right circular cylinder with length (height) $h = 7.4$ cm and diameter $d = 2.6$ cm. We want to find the volume of the cylinder in cubic centime

1. **State the problem:** We have a right triangle AOB with right angle at O, OA = 12 cm, OB = 5 cm. We need to find angle BAO and the area of the shaded region between two arcs ce

1. **State the problem:** Melur walks along the path A to B, then B to C, then C to A. We know distances AB = 3.6 km, AC = 8.4 km, and bearings: B from A is 054°, C from B is 132°.

1. **State the problem:** Find the distance between the points $(-12,1)$ and $(12,-1)$.\n\n2. **Recall the distance formula:** The distance $d$ between two points $(x_1,y_1)$ and $

1. The problem is to find the distance between the points $Y(-3,5)$ and $X(7,1)$.\n\n2. Use the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$: $$d = \sqrt{(x_2 -

1. **State the problem:** We need to find the distance between the two points $(-3, 5)$ and $(7, -1)$ on the coordinate plane. 2. **Recall the distance formula:** The distance $d$

1. The problem is to find the distance between the points $(-3,5)$ and $(7,1)$ using the distance formula. 2. The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. **State the problem:** Find the distance between the points $(-2,5)$ and $(4,-3)$.\n\n2. **Recall the distance formula:** The distance $d$ between two points $(x_1,y_1)$ and $(x

1. **Problem 1:** Find the radius of a circle with area 24 cm² and sector BAC area 3 cm². 2. The area of a circle is given by $$A = \pi r^2$$.

1. **Problem 26:** Find the radius $r$ of a circle with area 24 cm$^2$ and sector BAC area 3 cm$^2$. 2. The area of a circle is given by $$A=\pi r^2.$$ Given $$24=\pi r^2,$$ solve

1. **State the problem:** We are given a triangle ABC with sides AC = 7 cm, BC = 10 cm, and angle BAC = 65°. We need to find the size of angle ABC to the nearest 0.1°. 2. **Identif

1. Let's start by stating the problem: We need to create and analyze three types of circle problems involving secants and tangents: intersecting circles, secant-secant, and secant-