📐 geometry

1. **Problem statement:** We have a right triangle with hypotenuse length 15 feet. One leg is 3 feet longer than the other leg. We need to find the lengths of the two legs. 2. **Fo

1. **Problem Statement:** Find the perimeter of trapezoid WXYZ with sides WX = 3 cm, XY = 2.5 cm, YZ = 6.5 cm, and WZ = 5.2 cm. 2. **Formula for Perimeter:** The perimeter $P$ of a

1. **State the problem:** Given triangle MTL with MT \cong LT and OT bisects \angle MTL, prove that OT \perp LM. 2. **Given information:**

1. The problem asks to identify which pair is C.P.C.T.C., which stands for Corresponding Parts of Congruent Triangles are Congruent. 2. C.P.C.T.C. applies when two triangles are pr

1. **Problem Statement:** Prove that the altitude $AD$ of triangle $ABC$ is smaller than sides $AB$ and $AC$. Given $\angle BAC = 60^\circ$, $AC = 5$ cm, and $AD$ is the altitude f

1. **Problem Statement:** Given trapezium ABCD with AD || BC, AB = AD, BD = BC, and angle Ĉ = 80°. We need to determine the unknown angles.

1. Задача: Найти площадь боковой поверхности правильной усеченной пирамиды с основаниями $4\sqrt{3}$ и $10\sqrt{3}$, при угле между апофемой и основанием $60^\circ$. 2. Формулы и о

1. **Problem Statement:** We have a pentagon inscribed in a circle with given angles 25°, 32°, and 80°, and two unknown angles labeled \(\alpha\) and \(b\). We need to find the val

1. **State the problem:** We are given a triangle with three angles: 31°, 35°, and an unknown angle $x$. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:*

1. **Stating the problem:** We have two triangles with angles given as follows: - First triangle angles: $(5x - y)^\circ$ and $(3x + y)^\circ$.

1. **Stating the problem:** We are given two triangles with angles expressed in terms of $x$ and $y$, and some numerical angles. We need to verify angle relationships and solve for

1. **Problem Statement:** We are given three sets of information involving variables $x$ and $y$ related to angles in triangles and equations.

1. **Problem statement:** We need to find the height of an equilateral triangle with side length 7.4 m. 2. **Formula:** For an equilateral triangle with side length $a$, the height

1. **State the problem:** We need to find the area of a right triangle with a base of 17 m and an angle opposite to the base of 22º. 2. **Formula for the area of a triangle:** The

1. **State the problem:** We need to find the area of a right triangle with a base of 89 m and an angle adjacent to the base of 26º. 2. **Formula for the area of a triangle:** The

1. Problem (a): Find the number of planes of symmetry of the cuboid with edges AB = 8 cm, BC = 4 cm, and CR = 5 cm. 2. Explanation: A cuboid has planes of symmetry that divide it i

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \( (15x + 8)^\circ \) and \( (9x + 26)^\circ \). We need t

1. **Problem Statement:** Calculate the angle between line segment $AP$ and the rectangular base $ABCD$ of the triangular prism. 2. **Given Data:**

1. **State the problem:** We are given two parallel lines EF and CD cut by a transversal AB. Angle G is $(85 - 2x)^\circ$ and angle H is $(93 - 4x)^\circ$. Both angles are on the s

1. **State the problem:** We have a right triangle with a base of length 9 and a hypotenuse of length $10 \times \text{pipe size}$. There is an angle of 48 degrees inside the trian

1. **State the problem:** We have a right triangle with legs 9 and $10 \times \text{pipe size}$. We need to find the length TO, which is likely the hypotenuse of this right triangl