📐 geometry

1. **Problem statement:** Given a rectangular prism ABCD.A'B'C'D', a plane parallel to the side ABB'A' intersects edges AD, BC, A'D', B'C' at points M, N, M', N' respectively.

1. The problem asks which triangle among A, B, C, D, E, and F is similar to triangle T. 2. Two triangles are similar if their corresponding angles are equal and their corresponding

1. **State the problem:** Find the midpoint coordinates of points P(4, 3) and Q(10, 9). 2. **Formula:** The midpoint $M$ of two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given by:

1. সমস্যাটি হলো: একটি বৃত্তের কেন্দ্র O এবং ব্যাসার্ধ 10 সেমি। AB একটি chord যার দৈর্ঘ্য 14 সেমি। কোণ AOB এর মান রেডিয়ান এককে নির্ণয় করতে হবে। 2. সূত্র: বৃত্তের কেন্দ্র O থেকে ch

1. **State the problem:** Calculate the area of a right triangle with legs measuring 5 cm and 8 cm. 2. **Formula:** The area $A$ of a right triangle is given by

1. **State the problem:** We need to find the area of the dotted blue triangle inside a rectangle with width 6 cm and height 4 cm. 2. **Formula for the area of a triangle:** The ar

1. **State the problem:** We have a right triangle with legs measuring 5 cm and 17 cm. We need to find the length of the hypotenuse. 2. **Formula used:** The Pythagorean theorem st

1. **State the problem:** We have a rectangle with an area of 99 square units and a width of 11 units. We need to find the length of its diagonal, rounded to the nearest tenth. 2.

1. **State the problem:** We have a right triangle ABC with a right angle at A. The hypotenuse BC is 36 cm, and the segment from A to the point where the inscribed circle touches t

1. **Stating the problem:** We are given two parallel lines O-S-P and Q-T-R intersected by a transversal M-S-T-N. At point S, the angle is labeled as $(2x + 55)^\circ$, and at poin

1. **State the problem:** We are given two parallel lines cut by a transversal, creating angles \( (6x + 12)^\circ \) and \( 132^\circ \). We need to solve for \( x \). 2. **Identi

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((52 - 2x)^\circ\) and \((22x + 88)^\circ\). We need to s

1. **State the problem:** We need to find the measure of angle $\angle MSP$ given two expressions for angles formed by a transversal intersecting two parallel lines. 2. **Given:**

1. **State the problem:** We need to find the measure of angle $\angle MSP$ given that $\angle MSP = (7x + 60)^\circ$ and $\angle QTR = (108 - 3x)^\circ$. Lines $OQ$ and $PR$ are p

1. **Problem Statement:** A solid metal cylinder of height 10 cm and diameter 14 cm is melted and recast into two cones with volumes in the ratio 3:4, both cones having height 10 c

1. **Problem statement:** We are given a quadrilateral TUVW with angles at T and V known: $\angle T = 102^\circ$ and $\angle V = 59^\circ$. Sides WT and UV are equal.

1. **Problem statement:** We are given a parallelogram KGHJ with angle $\angle K = 38^\circ$. We need to find the size of angle $\angle KGH$. 2. **Recall properties of parallelogra

1. **Problem Statement:** Find the values of $x$ and $y$ that make each quadrilateral a parallelogram based on the given diagonal segment lengths. 2. **Important Property:** In a p

1. **State the problem:** We are given the vertices of a triangle at points $(2,-4)$, $(-5,3)$, and $(-7,0)$. We need to plot these points and draw the triangle formed by connectin

1. **Problem Statement:** We have a right-angled triangle ABC with D and E as midpoints of AB and BC respectively. We want to determine which statements are sufficient to find the

1. **Problem statement:** We have a triangle with vertices at approximately (2,3), (5,3), and (5,7). The triangle is reflected across a vertical line, and two vertices of the refle