📐 geometry

1. **Problem Statement:** Measure the angles and calculate the side lengths of triangles ABC and PQR where

1. **Stating the problem:** We have two figures: Figur A is a rectangle with width $8 \cdot x$ cm and height $2 \cdot x$ cm. Figur B is an equilateral triangle with side length $7

1. **Stating the problem:** We have a large rectangle with width 17 and height 14. Inside it, there is a smaller rectangle centered inside with width 9 and height $x$.

1. **State the problem:** We have a large rectangle with width 47 and height 15, and a smaller rectangle protruding from the bottom center. The smaller rectangle's top horizontal s

1. **Problem statement:** We have a truss structure with base segments $a=3000$, $b=2500$, and a vertical segment $c=2300$. We need to find the lengths of the four bars $d$, $e$, $

1. **State the problem:** We need to graph and label the image of quadrilateral ABCD after a translation 4 units left and 3 units down. 2. **Given vertices:**

1. **State the problem:** We are given a rectangle with midpoints M and N on two sides and need to find the coordinates of the center C of the rectangle. 2. **Recall properties:**

1. **Problem Statement:** Draw the cross section formed by a vertical plane that divides the solid into two congruent parts.

1. **Stating the problem:** Find the number of faces (F), edges (E), and vertices (V) for each solid: tetrahedron and cube.

1. The problem asks to find the equivalent single dilation scale factor when performing two dilations centered at the origin: first with scale factor 3, then with scale factor \fra

1. **State the problem:** Calculate the surface area and volume of a 3D triangular prism-like solid with given edges: 10 ft, 13 ft, 8 ft, 9 ft, and height 7.6 ft.

1. **Problem Statement:** Find the surface area of each prism given the dimensions and nets. 2. **Formula for Surface Area of a Prism:**

1. **State the problem:** We need to find the measure of the major arc $XZY$ in circle $C$. The given arcs are $120^\circ$ and $40^\circ$. 2. **Understand the arcs:** The circle's

1. The problem is to draw the nets of a 3D shape, which means unfolding the shape into its 2D faces. 2. Nets help us visualize all the faces of a solid laid flat without overlappin

1. **Problem 1: Cube with edge length 4 1/2 in** - Given: edge length $s = 4 \frac{1}{2} = 4.5$ in

1. **Problem statement:** We have two square sheets of paper, each 6 cm by 6 cm.

1. **State the problem:** We need to find the total volume of a figure made of two types of rectangular prisms. 2. **Given dimensions:**

1. **State the problem:** We need to find the measure of segment $GH$ given that $EF = 12$, $FG = 8$, and $GH = -6 + 2x$. 2. **Use the tangent-secant theorem:** When a tangent and

1. Problem statement: We have a right triangle $\triangle ABC$ with $\angle A = 90^\circ$, side $AC = 4.8$ cm, and hypotenuse $BC = 7.2$ cm. We need to find the angles $\angle B$ a

1. **State the problem:** We are given a circle with circumference 18 cm. We need to find the area of a parallelogram whose base is half the circumference of the circle and whose h

1. **Stating the problem:** You asked how the segment DA equals 7.1 inches in the previous problem. 2. **Reviewing given data:** The original problem stated BC = 12 inches (diamete