📐 geometry

1. **Problem Statement:** Define a line segment and explain its properties with a detailed description. 2. A **line segment** is a part of a line that is bounded by two distinct en

1. **State the problem:** We have a square PQRS with diagonal PR. Points P and R are given as P(4,7) and R(8,-5). We need to find the equation of the line passing through points Q

1. The problem states that the sum of interior angles of a regular polygon is 10800 degrees. We need to find the number of sides $n$ of the polygon. 2. The formula for the sum of i

1. Таны асуусан асуудал нь координатын хавтгайн 1-р мөчид дүрс байгуулах тухай юм. 2. Координатын хавтгай нь $x$ ба $y$ тэнхлэгүүдээр хуваагдсан дөрвөлжин хавтгай бөгөөд 1-р мөч нь

1. The problem asks if the lengths 4.1 cm, 8.4 cm, and 1.3 cm can form a triangle. 2. To determine this, we use the triangle inequality theorem, which states that the sum of the le

1. **State the problem:** We need to find the volume of a cylindrical water bottle with radius $4$ cm and height $20$ cm. 2. **Recall the formula for the volume of a cylinder:**

1. The problem states that the abscissa (x-coordinate) of point $P$ is $-8$ and the ordinate (y-coordinate) is $19$. 2. The location of a point on the coordinate plane is given as

1. The problem asks to measure the sides of triangles ABC and DEF, then find the ratio of corresponding sides DEF:ABC. 2. To determine if triangles ABC and DEF are the same shape,

1. **Problem 13:** Given a triangle with side $p=8$ cm, angle $P=40^\circ$, and angle $Q=65^\circ$, find side $q$ using the Sine Rule. 2. The Sine Rule states: $$\frac{p}{\sin P} =

1. The problem states that point E has an x-coordinate that is not 0 and a y-coordinate that is negative. 2. Recall the signs of coordinates in each quadrant:

1. **Problem statement:** Given triangle ABC with line AD perpendicular to CB, equation of AD is $y = x - 1$, coordinates of A are $(8, a)$, and D is $(2, 1)$. Find (i) value of $a

1. **State the problem:** Find the equation of the perpendicular bisector of the line segment joining points $A(2,9)$ and $B(10,5)$, and then find the coordinates of the point $Q$

1. The problem asks for the coordinates of point B. 2. The graph description only provides coordinates for points A and M: A is at (-7, -7) or approximately (-7, -6), and M is at (

1. Problem (a): Find the area of quadrilateral ABCD given vertices A(8, -4), B(7, 1), C(-5, 3), D(-4, -6) and area of triangle ABC = 29. Step 1: Calculate area of triangle ABC usin

1. **Problem:** Solve for $x$ given the proportion $$\frac{6}{3} = \frac{x}{5}$$. 2. **Step 1:** Simplify the left side: $$\frac{6}{3} = 2$$.

1. **State the problem:** We need to find the base and height of a triangle where the base is 4 cm less than twice its height, and the area is 60 cm². 2. **Define variables:** Let

1. **State the problem:** We need to find the size of angle $t$ in an irregular pentagon with given angles: $129^\circ$, $117^\circ$, $40^\circ$, $40^\circ$, and $137^\circ$. There

1. **Problem statement:** We have a rhombus with angles labeled 135°, $y$, 45°, and 315°. We need to find the size of angle $y$ and observe the relationship between opposite angles

1. **State the problem:** We have a six-pointed star made up of 6 identical quadrilaterals. Each quadrilateral has angles labeled $x$ and two angles of $35^\circ$. We need to find

1. **State the problem:** We have a square piece of cardboard 2 ft wide. We cut out a square of side length $x$ from each corner and fold up the sides to form an open box. We want

1. **State the problem:** We have a right-angled triangle ABC with right angle at B. Point P lies on BC such that BP = 4 cm and PC = 6 cm, so BC = 10 cm. The hypotenuse CA = 8 cm.