📐 geometry

1. The problem is about proving that all angles formed by bisectors of angles are equal. 2. When an angle is bisected, it is divided into two equal parts. This means each formed an

1. **State the problem:** Prove that a parallelogram whose diagonals are congruent has a right angle. 2. **Given:** In parallelogram $ABCD$, $\overline{AB} \parallel \overline{CD}$

1. **Problem Statement:** Find the measures of the angles of the triangle with vertices A(-1,0), B(2,1), and C(1,-2). 2. **Formula and Rules:** To find the angles of a triangle giv

1. The problem is to understand and explain the properties of a triangle. 2. A triangle is a polygon with three edges and three vertices.

1. Bài toán yêu cầu chứng minh các tính chất hình học trong hình chữ nhật ABCD với các điểm H, M, N, I được xác định như sau: 2. Ta có hình chữ nhật ABCD, AH vuông góc với BD tại H

1. Bài toán yêu cầu tìm tỉ số $\frac{SQ}{SA}$ trong hình chóp $SABCD$ với đáy là hình bình hành tâm $O$. Các điểm $M, N, P$ lần lượt là trung điểm của các đoạn $BC, CD, SD$. Điểm $

1. **Problem statement:** Given triangle ABC with AM as the median. Ray MD bisects angle AMB, ray ME bisects angle AMC, and I is the intersection of DE and AM. 2. **To prove:**

1. Bài toán: Cho hình chóp SABCD có đáy là hình bình hành tâm O. Trên cạnh SA lấy điểm M sao cho MA=2MS. Một phép chiếu song song theo phương MO lên mp(ABCD) biến điểm S thành điểm

1. Bài toán: Cho hình chóp $SABCD$ có đáy là hình bình hành tâm $O$. Trên cạnh $SA$ lấy điểm $M$ sao cho $MA=2MS$. Một phép chiếu song song theo phương $MO$ lên mặt phẳng $(ABCD)$

1. **Problem statement:** Construct triangle POR with $PQ=8cm$, $\angle QPR=45^\circ$, and $PR=6cm$. 2. **Step 1: Draw base PQ.** Draw a line segment $PQ=8cm$.

1. The problem asks to identify the chord in the given circle diagram. 2. A chord in a circle is a line segment with both endpoints on the circle's circumference.

1. The problem asks to identify the shaded part of a circle formed by two points A and B on the circumference and the center O, with the angle at O marked as $\alpha$. 2. The shade

1. **Stating the problem:** We are given a circle with center O and points A, B, C, D, E on the circumference. We know three arc angles near point E: 12°, 14°, and 73°, and we need

1. Problem: Determine if the given pairs of triangles are congruent and by which theorem. 2. Recall the congruence theorems:

1. The problem is to understand how to name congruent triangles. 2. Congruent triangles are triangles that have exactly the same size and shape.

1. The problem asks to identify the congruence criteria for the given triangles in part (a). 2. In part (a), triangles ABC and EFD are shown with two pairs of sides marked congruen

1. **Problem statement:** A right triangle with hypotenuse $\sqrt{3}$ meters is revolved about one of its legs to form a right circular cone. We need to find the radius $r$, height

1. **Problem:** Find the area of an isosceles triangle with two equal sides of length 5 cm each and the unequal side of length 8 cm. 2. **Formula:** The area of a triangle can be f

1. **State the problem:** We need to find the lateral surface area of a square pyramid with base side length $3.11$ m and height $7.22$ m. 2. **Formula for lateral surface area of

1. **State the problem:** Find the total surface area of a cone with radius $r=3.78$ m and height $h=2.15$ m. 2. **Formula:** The total surface area $A$ of a cone is given by:

1. **Problem Statement:** Understand and practice concepts on Points, Lines & Planes, Angles, Angles formed by two parallel lines, Introduction to Geometrical Construction, Perpend