📐 geometry

1. It seems you are asking about the methods used in solving a problem or in mathematics in general. 2. Geometric reasoning involves understanding properties and relationships of s

1. Let's state the problem: We have a quadrilateral with 4 equal sides and one angle of 90 degrees. We need to determine if this quadrilateral must be a square. 2. A quadrilateral

1. প্রশ্নটি বোঝা: জমির প্রস্থ কত? এখানে জমির প্রস্থ নির্ণয় করতে হবে। 2. সাধারণত, জমির আয়তনের ক্ষেত্রে প্রস্থ এবং দৈর্ঘ্যের তথ্য প্রয়োজন। প্রশ্নে শুধুমাত্র প্রস্থ জানতে চাওয়া হয

1. **State the problem:** Given a quadrilateral ABCD with four equal sides (AB = BC = CD = DA) and one right angle (\(\angle DAB = 90^\circ\)), determine if ABCD is a square.

1. সমস্যাটি হলো একটি আয়তাকার জমির দৈর্ঘ্য প্রস্থের দ্বিগুণ এবং জমির পরিসীমা ১২০ মিটার। এখানে জমির ভিতরে চারদিকে সমান পাড়বিশিষ্ট ২ মিটার বিস্তৃত একটি পুকুর রয়েছে। পুকুরের গভীরতা ৫ ম

1. **Given problem:** We have a circle with points on its circumference and angles 43° and 76°, and we need to find the reflex angle $z$. 2. **Understanding the problem:** The refl

1. Bài toán yêu cầu tính chu vi hàng rào của một mảnh vườn hình chữ nhật với chiều dài $x$ và chiều rộng $y$, biết hàng rào có chu vi $120$ mét và diện tích $S=xy$ lớn nhất. 2. Ta

1. First, to find the total area of the lot, we need specific information about the shape and dimensions of the lot. 2. Commonly, lots are rectangular or irregular polygons, so the

1. **State the problem:** We have a lot shaped as a polygon with corners 1, 2, 3, and 4. We know azimuths and distances for lines 2-3, 3-4, and 3-1, but distances and azimuths for

1. The problem asks to find the measure of an exterior angle of a regular hendecagon, which is an 11-sided polygon. 2. The sum of the exterior angles of any polygon is always 360 d

1. Given that triangle ABC is congruent to triangle PQR, with \(\angle BAC = \angle QPR\), find the side in triangle PQR that is equal to side BC in triangle ABC. Step 1. By the de

1. The problem is to find the measure of an exterior angle of a regular hexadecagon, which is a polygon with 16 sides. 2. The sum of the exterior angles of any polygon is always $3

1. We are given a square with center 150, top 100, left 150, right 50, bottom 150. To verify, note the center should be the average of left and right, and top and bottom. Calculate

1. We are asked to find the measure of an exterior angle of a regular octagon. 2. A regular octagon has 8 equal sides and 8 equal exterior angles.

1. The problem is to find the measure of each interior angle of a regular octagon (8-sided polygon). 2. We know the number of sides $n=8$ and the sum of exterior angles of any poly

1. **Problem statement:** Given a regular polygon with $n$ sides, each exterior angle is labeled as $\alpha$. You are asked to verify the relationship $\sum \alpha_i = n \cdot 180^

1. The problem describes four instances of triangles with labeled side lengths and bases, along with rectangles labeled with time or distance units. 2. We need to analyze the trian

1. Let's clarify the problem: "shortest way" can refer to finding the shortest distance between two points, the shortest path in geometry, or the shortest method to solve a problem

1. **State the problem:** In triangle $\triangle ABC$, a line parallel to side $BC$ meets $AB$ and $AC$ at points $P$ and $Q$, respectively. Given that $AP = QC$, $AB = 12$ cm, and

1. **Problem 7: Find the area of figure ABCDEFGH**. Given: AC = HF = $\sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3$ cm.

1. **Problem 7:** Find the area of figure ABCDEFGH. Given: