📐 geometry

1. The problem is to find the image of point $A=(-1,0)$ after reflection on the $y$-axis. 2. Reflection on the $y$-axis changes the $x$-coordinate of a point to its opposite, while

1. **State the problem:** We have a sector OAB of a circle with central angle $131^\circ$ and arc length $192$ cm. We need to find the radius $r$ of the circle. 2. **Recall the for

1. **State the problem:** We have a sector OAB of a circle with a central angle of $131^\circ$ and an arc length of 192 cm. We need to find the radius $r$ of the circle to 2 decima

1. **State the problem:** We have a circle with center $P$ and points $A, B, C, D, E$ on the circle in clockwise order. $\overline{AD}$ and $\overline{BE}$ are diameters. We want t

1. **State the problem:** We need to find the surface area of a triangular prism with triangle sides 26 yd and 19 yd, prism height 10 yd, and base length 24 yd. 2. **Identify the s

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 8 ft and 12 ft, and legs of 18 ft and 4 ft. 2. **Identify the bases and height:** The two pa

1. **State the problem:** We have a rectangular prism storage container with dimensions 7 m, 5 m, and 2 m. The total cost of the sheet steel used for the surface area is 4484. We n

1. **State the problem:** We have a kite WXYZ with diagonals XZ and WY intersecting at V. Given that $XZ = 18$ and $WY = 52$, and the sides WX, XZ, WY are labeled as follows: $XZ =

1. The problem asks if there is a way to solve geometry problems without using similar triangles. 2. Similar triangles are often used because they allow us to find unknown lengths

1. **State the problem:** We need to calculate the length of segment $FG$ in the given geometric figure. 2. **Analyze the figure:** We have a right triangle $DEF$ with right angle

1. **State the problem:** We are given three angles formed by intersecting lines with expressions $(8x - 10)^\circ$, $(6y + 20)^\circ$, and $(7x)^\circ$. We need to find the values

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

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