📐 geometry

1. **State the problem:** We are given diameters and circumferences of circles and need to calculate the ratio $\frac{C}{d}$ for each to the nearest hundredth. 2. **Formula:** The

1. **Stating the problem:** We have a quadrilateral ABCD with given sides and angles, and we need to find the unknown angle $\theta$ at vertex D.

1. **State the problem:** We are given that $\angle NOT \not\cong \angle POV$, $O$ is the midpoint of segment $NP$, and $\angle N \cong \angle P$. We need to prove that segment $ST

1. **Problem statement:** Given lines $k$ and $\ell$ are parallel, and the measure of angle $ABC$ is 19 degrees. 2. **Part a:** Explain why the measure of angle $ECF$ is 19 degrees

1. **Problem:** Find the measures of angles $\angle ABC$, $\angle EBD$, and $\angle ABE$ given that $\angle ABC = 50^\circ$. 2. **Given:** $\angle ABC = 50^\circ$.

1. **Problem a:** Find the area of a circle with radius 6.8 cm. 2. The formula for the area of a circle is:

1. The problem states that Darren has a piece of wood measuring 7 inches by 8 inches, which forms a large rectangle. 2. To divide this large rectangle into two smaller rectangles,

1. **State the problem:** We have a dartboard with a diameter of 18 inches. We need to find its radius and circumference. 2. **Recall formulas:**

1. **Find the circumference of a circle with diameter 5.9 ft.** The formula for circumference is $$C = \pi d$$ where $d$ is the diameter.

1. **Problem statement:** Given trapezium WXYZ with WX \parallel ZY, rhombus AXYB inside it, and lines XBC and XAZ straight. Given angles: $\angle XAB=82^\circ$, $\angle ZYB=19^\ci

1. **Problem Statement:** We have a rhombus with diagonals intersecting inside it, creating four smaller angles numbered 1, 2, 3, and 4. One of the outer angles of the rhombus meas

1. **State the problem:** We have two circles given by their equations:

1. **Problem statement:** Find the measures of the numbered angles 1, 2, 3, and 4 inside the rhombus, given one angle of the rhombus is 39°. 2. **Key properties of a rhombus:**

1. **Problem statement:** Find the measures of the numbered angles in the rhombus given the side lengths and angle markings. 2. **Recall properties of a rhombus:**

1. **Problem:** Calculate the length of AG in the first figure (a prism with base AB = 8, height 8, depth 8). 2. **Formula and rules:** To find the length of a diagonal in a rectan

1. **Problem statement:** Use Pythagoras' theorem to find the unknown length in each right triangle given the two legs. 2. **Formula:** For a right triangle with legs $a$ and $b$,

1. 問題の確認：三角形の相似条件を使って、相似な三角形の組を3組見つけ、記号\(\sim\)で表す。 2. 相似条件の復習：

1. **State the problem:** We have a right pyramid with a square base of side length 10 cm and sloping edges of length 17 cm. The perpendicular height drops from the apex to the cen

1. The problem is to find the answer for a triangle, but the specific question is not stated. Common triangle problems include finding the area, perimeter, or missing sides or angl

1. **Problem statement:** We have two similar shapes (cylinders) with given surface areas and volumes. The smaller shape has surface area $110$ mm² and volume $75$ mm³. The larger

1. **Problem 4:** Find the length of side $DF$ in triangle $DEF$ or state what additional information is needed. 2. Given triangle $DEF$ with angles $D=56^\circ$, $E=39^\circ$, and