📐 geometry

1. **State the problem:** Determine if triangles △LMN and △PQR are similar, congruent, or neither using side lengths. 2. **Given side lengths:**

1. **Problem Statement:** We are given two triangles △LMN and △XYZ with some side lengths known. We want to prove that △LMN ~ △XYZ by the SSS (Side-Side-Side) similarity theorem. 2

1. **State the problem:** We need to find the shortest distance from point Q to the line segment PR in triangle PQR. 2. **Given data:**

1. **Problem Statement:** We have two right-angled triangles joined by a common side. One triangle has an angle of 60° and a vertical side labeled $n$. The other triangle has angle

1. **State the problem:** Calculate the volume of a square-based pyramid with base dimensions 23 cm by 16 cm and a slant height of 34 cm. 2. **Formula for volume of a pyramid:**

1. **Problem Statement:** (a) Explain the difference between capacity and volume to Grade 6 pupils.

1. **Problem Statement:** (a) Explain the difference between capacity and volume to Grade 6 pupils.

1. **Problem Statement:** Given two parallel lines $O$ and $m$ cut by a transversal $k$, find the values of angles $z$ and $x$ where the angles are $(3x + 15)^\circ$, $z^\circ$, an

1. **State the problem:** We need to find the perimeter of a right triangle with legs of lengths $\sqrt{27}$ cm and $\sqrt{3}$ cm. 2. **Recall the formula:** The perimeter $P$ of a

1. **State the problem:** We have a trapezium with area $6\sqrt{21}$ cm², a top side of 5 cm, a height of $\sqrt{7}$ cm, and a base labeled $f$ cm. We need to find $f$ in the form

1. **Problem Statement:** We have triangle $\triangle ABC$ with vertices $A(-11, 2)$, $B(3, -5)$, and $C(6, 1)$. We need to:

1. **Problem Statement:** Calculate various properties of triangle $\triangle ABC$ with vertices $A(-11,2)$, $B(3,-5)$, and $C(6,1)$.

1. **Problem statement:** We are given a straight horizontal line with two angles adjacent to it: one is 50° on the left side, and the other is 35° on the right side. We need to fi

1. **Problem Statement:** We have a right triangle with legs 24 and $x$, and the hypotenuse divided into two segments of lengths 12 and 18. We need to find the value of $x$. 2. **U

1. Muammo: faqat to'g'ri burchakli uchburchaklar haqida gaplashamiz. 2. To'g'ri burchakli uchburchakda bitta burchak $90^\circ$ ga teng.

1. **Problem Statement:** Identify the type of angle pairs in each diagram (8 to 15) as corresponding, alternate interior, alternate exterior, same-side interior, vertical, or line

1. **State the problem:** We need to prove that two lines are parallel when they are cut by a transversal. 2. **Key concept:** When a transversal cuts two lines, certain angle pair

1. **Problem Statement:** We have two triangles, △ABC and △A'B'C', where △A'B'C' is a scaled copy of △ABC. We know the sides of △ABC: AB = 5, BC = 2, AC = 6, and the sides of △A'B'

1. **Problem Statement:** A solid cylinder has radius 18 cm and height 15 cm. A conical hole of radius $r$ cm and depth 12 cm is drilled on one end. The volume of the material remo

1. **Problem Statement:** We have a 30-inch by 16-inch piece of cardboard. Squares of side length $x$ are cut from each corner, and the sides are folded up to form an open box. We

1. **Problem Statement:** Given two parallel lines AB and CD, with angles \(\angle BNO = 128^\circ\) and \(\angle COM = 56^\circ\), find \(\angle MON\) and \(\angle DON\).\n\n2. **