📐 geometry

1. **Problem statement:** We have a right triangle with a 30° angle, hypotenuse length 8, and sides opposite and adjacent to the 30° angle labeled $y$ and $x$ respectively. We need

1. **Problem Statement:** We have a right triangle with a 30° angle, the side opposite this angle labeled $y$, the hypotenuse labeled 8, and the adjacent side labeled $x$. We need

1. **Problem Statement:** We have a special right triangle with angles 45°, 45°, and 90°, where the hypotenuse is given as $7\sqrt{2}$. We need to find the lengths of legs $x$ and

1. **Problem statement:** We are given triangle PQR with sides $PQ=1.6$ cm, $PR=4.2$ cm, and angle $\angle PRQ=18^\circ$. We know $\angle PQR$ is obtuse and need to find the area o

1. **State the problem:** We have a scale drawing where 1 cm represents 2 m in real life.

1. **State the problem:** We have a scale drawing where 1 cm represents 2 m in real life.

1. **Problem Statement:** We have two similar triangles ABC and PQR with corresponding sides AB to PQ and AC to PR.

1. **State the problem:** We have a parallelogram ABCE with diagonals AC and EB intersecting at point D. We want to understand the relationships between the sides, angles, and segm

1. **State the problem:** Prove that the diagonals of parallelogram GHJK bisect each other, i.e., show that $\overline{GL} \cong \overline{JL}$ and $\overline{HL} \cong \overline{K

1. **State the problem:** Given parallelogram $ABCD$, prove that $\overline{AD} \cong \overline{CB}$ and $\overline{AB} \cong \overline{CD}$. 2. **Recall the given information and

1. **Problem 11: Rectangle JKLM with diagonals intersecting at N** Given: Rectangle JKLM, diagonals intersect at N.

1. **Problem 1: Rectangle JKLM with diagonals intersecting at N.** Given: $JN = x + 3$ and $JL = 3x + 1$. We need to find which values among A to E are correct.

1. **State the problem:** We need to find the area of a compound figure composed of several rectangles and squares with given side lengths. 2. **Identify the shapes and their dimen

1. **State the problem:** We need to find the total surface area of a solid cylinder with radius $r = 5.1$ cm and height $h = 3.7$ cm. 2. **Formula for total surface area of a cyli

1. **State the problem:** We need to find the surface area of a cylinder with radius $r=4$ cm and height $h=9$ cm, using $\pi = 3.14$. The surface area includes the areas of the tw

1. **Problem Statement:** Given a triangle with points A, B, C, D, E, F, G such that AB = BC, BG = GF, and DE = EF, show that AG = 3GE.

1. **Problem Statement:** Given a geometric figure with points A, B, C, D, E, F, G, where AB = BC, BG = GF, and DE = EF, show that AG = 3GE. 2. **Given:**

1. **Problem Statement:** We have a parallelogram ABCD with diagonal BD. Points P and Q lie on sides AB and CD respectively such that angles labeled P2 and Q2 are equal.

1. **Problem statement:** We have two similar shapes A and B. Shape A has width 3 cm and height 6.5 cm. Shape B has width 12 cm and unknown height $h$. We need to find $h$. 2. **Fo

1. **State the problem:** Find the distance between two points in the coordinate plane. 2. **Formula:** The distance $d$ between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given

1. The problem involves identifying the coordinates of two points on a coordinate plane. 2. The first point is located in the top-right quadrant (Quadrant I) at coordinates $(1,1)$