📐 geometry

1. **State the problem:** Given that $\angle SUT \cong \angle YXZ$, prove that the vectors $\overrightarrow{WY}$ and $\overrightarrow{TV}$ are parallel. 2. **Analyze the given info

1. **State the problem:** We have a triangle with angles 96° and 25°, and the side opposite the 25° angle is 13 units. We need to find the side length opposite the 96° angle using

1. The problem is to prove a geometric property or theorem step by step. 2. First, clearly state the theorem or property to be proven.

1. **State the problem:** We have a circle with center O and tangent ABCD at point C.

1. **Problem Statement:** Prove the geometric relation $ (JL \times JG + HL \times HK) = (JH)^2 $ given the triangle $\triangle ABC$ with centroid $J$, median $BM$, altitude $AD$,

1. **Problem Statement:** We have an oval (ellipse) with radius $R=74$ and a square inside it with side length $S=46$. Points $a$, $b$, and $c$ are on these shapes, and we want for

1. **Problem statement:** We have a square with side length $S=46$ and an oval (ellipse) with radius $R=74$ intersecting the square vertically. Points $a$, $b$, and $c$ lie on the

1. **State the problem:** We are given two triangles, $\triangle ABC$ and $\triangle NLM$, with the conditions: - $m(\angle B) = m(\angle NLM)$

1. **State the problem:** We have a rectangle with width 10 m and height 8 m. Inside it, there is a parallelogram with base 2 m and height 8 m (matching the rectangle's height). We

1. **State the problem:** We need to find the area of the composite shape consisting of a large rectangle and a smaller attached rectangle (not a square since sides are 4 cm and 6

1. **State the problem:** We have a quadrilateral BACD with diagonals AD and BC drawn, dividing it into four triangles. Given that AB = BC = BD and BD is parallel to AC, and angles

1. **State the problem:** Find the obtuse angle between the hour and minute hands of a clock at 11:25 am. 2. **Calculate the minute hand angle:** The minute hand moves 6 degrees pe

1. **State the problem:** We need to find the perimeter of quadrilateral ADBC given that $AC=5$ cm, $BC=3$ cm, and $CB=DB$. 2. **Analyze the given information:** Since $CB=DB$, the

1. **State the problem:** We are given a cylinder with a radius of 7 cm and a total surface area of 572 cm². We need to find its height. 2. **Recall the formula for the surface are

1. **State the problem:** We have an isosceles trapezium with the shorter parallel side on top and the longer parallel side on the bottom. The bottom interior angles are each 60°.

1. نبدأ بتحديد المشكلة: لدينا نقطة A بإحداثيات (5, -2) ونقطة B بإحداثيات (4, -7). النقطة Q تقع على القطعة المستقيمة AB بحيث طول AQ يساوي ثلثي طول AB. 2. نحسب متجه AB:

1. نبدأ ببيان المشكلة: لدينا مثلث قائم الزاوية مع ضلعين طولهما 2 متر، والوتر طوله 3 متر، وزاوية 45 درجة عند النقطة A. 2. نلاحظ أن المثلث قائم الزاوية والوتر 3 متر، والزاوية 45 درجة

1. The problem states that a triangle has interior angles measuring $2c - 9^\circ$, $3c + 5^\circ$, and $c^\circ$. We need to find the value of $c$. 2. According to the Triangle An

1. **State the problem:** We have a triangle with three interior angles: $x + 11^\circ$, $5x$, and $x + 11^\circ$. We need to find the value of $x$. 2. **Recall the Triangle Angle-

1. **State the problem:** We have a triangle with three angles labeled as follows: - Top-left angle: $2a + 20^\circ$

1. The problem states that the three angles of a triangle are given as $2u + 7^\circ$, $3u + 4^\circ$, and $2u - 4^\circ$. We need to find the value of $u$. 2. Recall that the sum