📐 geometry

1. **State the problem:** We are given a figure with points A, H, D, C, B and the following data: $m(\angle AHD) = m(\angle C)$, $AH = 14$ cm, $HD = 12$ cm, $CB = 15$ cm, and $DB =

1. The problem involves a right-angle triangle divided into four smaller triangular plates with given areas and front segment lengths. 2. We are given the areas in Marla and square

1. **State the problem:** We need to find the perimeter of an L-shaped polygon on a grid where each unit corresponds to 1 cm. 2. **Analyze the shape:** The L-shape consists of a ve

1. **State the problem:** We need to find the perimeter of an L-shaped polygon on a grid where each square is 1 cm by 1 cm. 2. **Analyze the shape:** The shape covers 3 cm horizont

1. **State the problem:** We need to find the perimeter of an "L" shaped figure on a 6x6 grid where each grid square side is 1 cm. 2. **Identify the lengths of each side:**

1. Statement 36: The perpendiculars drawn from the vertices of a triangle to the opposite sides are known as the altitudes of the triangle. Conclusion I: The line segments joining

1. نُعطى النقاط: ا=(3,2)، ب=(-2,5)، ج=(-7,5)، د=(6,0). 2. المطلوب: إثبات أن القطعتين اج وبد ينصف كل منهما الآخر، أي أن نقطة منتصف اج هي نفسها نقطة منتصف بد.

1. The problem states that an equilateral triangle with side length $s$ is inscribed in a circle, and we need to find the radius $r$ of the circle in terms of $s$. 2. In an equilat

1. **State the problem:** We need to find the values of angles $a$, $b$, $c$, and $d$ in the cyclic quadrilateral $WXYZ$ inscribed in a circle, given the other angles at points $X$

1. The problem asks to find the length of the shortest side of the triangle in millimetres and the size of the largest angle. 2. Since the largest angle is given as 124°, the short

1. The problem states that $r(180^\circ, O)(\triangle ABC) = \triangle A'B'C'$, meaning $\triangle ABC$ is rotated 180 degrees about the origin $O$ to get $\triangle A'B'C'$. We ne

1. The problem asks to create an image of 5 options arranged in a triangular shape. 2. To visualize this, imagine placing the options as points forming a triangle.

1. **Problem Statement:** Divide a triangular plate with sides 176 ft (front), 107 ft, and 102 ft into four parts using three straight lines such that three parts are equal in area

1. The problem states: "AD = 3m, not AB". We need to understand the relationship between points A, B, and D. 2. Since AD is given as 3 meters, and AB is not equal to AD, we know AB

1. Stating the problem: We have a pyramid ABCS with base ABC being a right triangle with legs $|AB|=6$ and $|AC|=8$. The lateral edges $|AS|=|BS|=|CS|=10$. We need to find the volu

1. The problem asks to identify the major radius from the given options: 2.5, 4, 2, and 5. 2. The "major radius" typically refers to the larger radius in a system where two radii a

1. ප්‍රශ්නය: අරාව $a$ වන මෙනිස් බෝල් 3ක් එකිනෙකට ඉහළින් සෙපදවූ රැපුලේ ඉතිරි පරිමාව සොයා ගැනීම.

1. **State the problem:** We have two parallel lines \(a\) and \(b\) cut by two intersecting lines, creating angles labeled \(123^\circ\), \(81^\circ\), \(116^\circ\), \(x^\circ\),

1. **State the problem:** Kali has a 6 meter ladder leaning against a tree. The base of the ladder is 2 meters from the tree. We need to find how high the ladder reaches on the tre

1. **State the problem:** We have a right triangle with vertices Aurora, Burlington, and Clifton. The side Aurora-Burlington is 65 km, Burlington-Clifton is $x$ km, and the hypoten

1. Let's define the problem: We want to find how much closer the direct travel distance from Aurora to Clifton is compared to traveling from Aurora to Clifton via Burlington. 2. Su