📐 geometry

1. **State the problem:** Two students build boxes: one a cube with edge 60 cm, the other a rectangular prism with width $w$ cm, height 30 cm, and depth 45 cm. Both boxes have the

1. **Stating the problem:** Given the equations:

1. **Problem 8:** Convert 8.2 cm on a map with scale 1:10,000 to actual distance in meters. 2. The scale 1:10,000 means 1 cm on the map represents 10,000 cm in reality.

1. **State the problem:** We need to find the images of the given objects under specified transformations using the diagram and fill in the table.

1. **State the problem:** We need to find the sizes of angles $t$, $s$, and $r$ in a figure with three parallel lines cut by two transversals, given angles $48^\circ$ and $120^\cir

1. **State the problem:** We have two parallel lines cut by a transversal, creating angles labeled $r$, $s$, and $t$, with given angles $120^\circ$ and $48^\circ$. We need to find

1. **Problem 1: Work out the area of the shaded section when the radius of the circle is 7 cm.** 2. The shaded section is a quarter circle inside a square, so the area of the shade

1. The problem asks to draw three angles each measuring 55° but oriented differently. 2. The formula for an angle is the measure between two rays with a common vertex. Angles of th

1. **State the problem:** We need to find the measure of angle $\angle X$ in rhombus VWXY given that $m\angle W = 2p + 38^\circ$ and $m\angle V = 4p + 82^\circ$. 2. **Recall proper

1. **State the problem:** We have a parallelogram with preimage vertices at $(1,5)$, $(3,3)$, $(3,7)$, and $(5,5)$, and its image vertices at $(-5,3)$, $(-3,1)$, $(-3,5)$, and $(-1

1. The problem is to explain what a square is and draw it. 2. A square is a special type of quadrilateral where all four sides are equal in length and all four angles are right ang

1. The problem states that the angle $\angle ACB$ is half of the arc $\widehat{AB}$. This is a classic property in circle geometry. 2. The formula used here is the Inscribed Angle

1. **Stating the problem:** We have an L-shaped figure with dimensions given: the long horizontal part is 46 mm long and 12 mm high, the vertical segment is 30 mm high and 5 mm wid

1. **State the problem:** We need to find the areas of Rectangle A, Rectangle B, and Triangle C, then find the total area of the composite figure. 2. **Formulas used:**

1. **Problem statement:** Given that PQ is parallel to MN, LRT is an isosceles triangle with LR = RT, and SLT is a straight line, find the value of $x$. 2. **Key facts and formulas

1. **State the problem:** We are given points W, X, Y on a horizontal line with segments WX and XY labeled as $3n - 15$ and $2n + 5$ respectively. A vertical ray extends from X to

1. **State the problem:** We have a square with a line $m$ passing through one of its vertices, creating four angles at the intersection labeled $\angle 1$, $\angle 2$, $\angle 3$,

1. **State the problem:** We need to determine which transformation takes Triangle A, located in the bottom-right quadrant, to Triangle B, located in the top-left quadrant. 2. **Id

1. **State the problem:** We need to find the value of $\cos L$ in the right triangle $\triangle LKJ$ where $LK=5$, $KJ=7$, and the hypotenuse $LJ=\sqrt{74}$. The right angle is at

1. **State the problem:** We need to find the value of $\cos X$ in a right triangle $\triangle ZYX$ with a right angle at vertex $Y$. 2. **Identify the sides:** The triangle has ve

1. **Stating the problem:** We are given that the difference between two angles $\alpha$ and $\beta$ is 26°, i.e., $\alpha - \beta = 26^\circ$. We need to find the value of $x$ giv