📐 geometry

1. **State the problem:** We are given three angles related by a transversal intersecting two parallel lines: angles are $(8x - 10)^\circ$, $(6y + 20)^\circ$, and $(7x)^\circ$. We

1. **State the problem:** We are given a diagram with streets Maple Ave, 7th Ave, 2nd St, and 1st St intersecting. We know the angle between Maple Ave and 2nd St is 115°. 2. **Find

1. **State the problem:** We have an isosceles triangle with two equal sides of length 10 and a height (altitude) of 8 drawn from the top vertex to the base. We need to find the le

1. **State the problem:** We have an isosceles triangle with two equal sides of length $x$, a base of length 12, and a height of 8 drawn from the top vertex to the base. 2. **Analy

1. The problem involves an isosceles triangle with two equal sides of length 5 and a base of length 6. We need to find the length $x$ of the perpendicular line from the apex to the

1. **State the problem:** We have an isosceles triangle with two equal sides each of length $\sqrt{52}$ and a base of length 8. The height $x$ is drawn from the apex to the midpoin

1. **State the problem:** We have an isosceles triangle with two equal sides each of length $\sqrt{74}$, a height (altitude) of length 7, and the base divided into two equal segmen

1. **State the problem:** We have a right triangle with legs of lengths 7 and 9, and the hypotenuse labeled $x$. We need to find the value of $x$. 2. **Recall the Pythagorean theor

1. **State the problem:** We have a right triangle with hypotenuse 9, one leg 8, and the other leg $x$. We need to find the value of $x$. 2. **Use the Pythagorean theorem:** For a

1. The problem states we have a right triangle with legs 12 and 16, and hypotenuse $x$. 2. By the Pythagorean theorem, $x^2 = 12^2 + 16^2$.

1. The problem is to find the value of $x$ in a right triangle where the vertical side is 2, the horizontal side is 10, and $x$ is the hypotenuse. 2. According to the Pythagorean t

1. The problem states we have a right triangle with legs of lengths 5 and 12, and the hypotenuse labeled as $x$. 2. By the Pythagorean theorem, in a right triangle, the square of t

1. **State the problem:** We are given two angles, \(\angle A = 6x - 35^\circ\) and \(\angle B = 3x + 53^\circ\), formed by two parallel lines crossed by a transversal. We need to

1. The problem gives two angles formed by a transversal cutting two parallel lines: \(\angle A = 6x + 18^\circ\) and \(\angle B = x + 93^\circ\). These angles are interior angles o

1. The problem gives two angles \(\angle A = 6x - 18^\circ\) and \(\angle B = 14x + 38^\circ\) formed by a transversal intersecting two parallel lines. 2. Since \(\angle A\) and \(

1. **Exercice 1** Énoncé : Dans un triangle avec BC = 6, AE = 2, AB = 5, et (EF) // (BC).

1. The problem is to translate rhombus CDEF 4 units left and 13 units down on the coordinate plane. 2. The original coordinates are:

1. The problem asks us to translate the polygon 5 units to the right. 2. Translation 5 units right means adding 5 to the x-coordinate of each vertex, while the y-coordinate remains

1. **State the problem:** We need to find the coordinates of the vertices E', F', G', and H' after a 180° counterclockwise rotation around the origin. 2. **Recall the rotation rule

1. **State the problem:** We have a right pyramid with a regular pentagonal base of side length 20 cm, vertical height 80 cm, and all slant edges equal. We need to find the total s

1. **State the problem:** We need to find the distance between points A(3, -1) and B(-1, 4). 2. **Recall the distance formula:** The distance $d$ between two points $(x_1, y_1)$ an