📐 geometry

1. **State the problem:** We are given a diamond-shaped quadrilateral EFGH with sides EF = FG = GH = HE. We need to prove that triangle EHF is congruent to triangle GHF. 2. **Analy

1. **State the problem:** We need to prove that triangle EHF is congruent to triangle GHF given that EF = FG = GH = HE. 2. **Given information:** All sides EF, FG, GH, and HE are e

1. Problem 8(a): Two intersecting lines with angles 52°, 35°, and x. - Since vertical angles are equal, and the sum of angles around a point is 360°, we find $x$ by:

1. **State the problem:** We have a right triangle formed by the wall, the floor, and the tube. The wall is vertical with length 2.7 m, the floor is horizontal with length 3.6 m, a

1. সমস্যাটি হলো, চিত্রে দেওয়া হয়েছে \(\angle PQR = 55^\circ\), \(\angle LRN = 90^\circ\), এবং \(PQ \parallel MR\)। আমাদের \(\angle MRN\) এর মান নির্ণয় করতে হবে। 2. যেহেতু \(PQ \

1. The problem asks which rule explains why the two triangles TUV and XWY are congruent. 2. The Side-Angle-Side (SAS) congruence rule states that if two sides and the included angl

1. The problem involves constructing scale drawings based on a square with side length 6 units on a grid and a scale reference of 18 meters. 2. Each side of the square measures 6 u

1. The problem describes a square with each side measuring 6 units. 2. Since all sides of a square are equal, the side length is 6.

1. **State the problem:** Write the equation in standard form for the circle with diameter endpoints at $\left(\frac{19}{2}, \frac{15}{2}\right)$ and $\left(\frac{11}{2}, \frac{21}

1. نبدأ بكتابة معطيات المسألة: النقطة م = (0, 300) والمستقيم معادلته: $$y = 1043 + k(42 - 141)$$ 2. نعيد كتابة معادلة المستقيم بشكل أبسط. الفرق في الإحداثيات هو: $$42 - 141 = -99$$

1. نُعطى متجهين اتجاهيين للمستقيمين: $$\vec{u} = \left(\frac{13}{12}, 0, 0\right), \quad \vec{v} = \left(\frac{7}{3}, -\frac{2}{3}, \frac{4}{3}\right)$$

1. **State the problem:** Given that triangles $\triangle ADB$ and $\triangle BCA$ are congruent, prove that segments $DE$ and $CE$ are congruent. 2. **Given:** $\triangle ADB \con

1. The problem states that the circumference of a circle is 24 cm, and we need to find the area of the circle in terms of $\pi$. 2. Recall the formula for the circumference of a ci

1. **State the problem:** We need to find the area of a trapezium with parallel sides of lengths 3.641 and 2.996 units, and a width (distance between the parallel sides) of $\frac{

1. **State the problem:** We need to find the arc measure of the major arc \(\overset{\frown}{BAD}\) on circle \(P\) in degrees. 2. **Identify given information:** The central angl

1. **State the problem:** We have a triangle with two sides measuring 7.5 cm and 8.9 cm, and the angle between them is 78°. We need to find the length of side $d$ opposite the 78°

1. Задачата е да се определи пресечната права на рамнините T и P. 2. Рамнината T е дефинирана со точка T(-50,30,30) и рамнината P со точка P(30,-60,50).

1. مسئله: در متوازی الاضلاع ABCD طول BH را بیابید. 2. ابتدا باید بدانیم که BH عمود بر کدام ضلع است. در متوازی الاضلاع، ارتفاع از یک رأس به ضلع مقابل عمود است.

1. **Problem statement:** We need to find the area of the shaded sector of a circle where the central angle $\theta = 56^\circ$ and the circumference $C = 31.416$ cm. 2. **Find the

1. **State the problem:** Lee wants to paint the front face and top face of a cuboid. The front face measures 54 cm by 32 cm, and the top face measures 32 cm by 28 cm. The paint co

1. **State the problem:** We are given a circle with points A, B, C, and D on its circumference. Triangle ABD has an angle at vertex A of 56° and triangle BCD has an angle at verte