📐 geometry

1. **State the problem:** We are given that $DE$ bisects $\angle ABC$, and the measures of $\angle ABC$ and $\angle DBC$ are given as $(7x+29)$ degrees and $99$ degrees respectivel

1. The shape described is an irregular rounded closed figure, resembling a blob or a three-lobed figure. 2. It has a couple of interior curved or diagonal line segments.

### 5. feladat: Vektor EF meghatározása az a és b vektorok segítségével 1. **Probléma megfogalmazása:**

1. **State the problem:** We need to find the point $P$ on the plane given by the equation $$2x + 3y - z = 1$$ that is closest to the point $(2, 1, 0)$, and then find the distance

1. The problem asks for the change in width of segment $AB$. 2. To find the change in width, we need the initial and final widths of $AB$ or a formula relating the width to other v

1. **State the problem:** We need to find the gradients (slopes) of sides $AB$ and $CD$ of the parallelogram $ABCD$ with points $A(2,2)$, $B(8,6)$, $C(6,8)$, and $D(0,4)$. 2. **For

1. **State the problem:** We need to find what percentage of the whole square is shaded. 2. **Understand the figure:** The figure is a square grid with a yellow shaded shape occupy

1. **State the problem:** We are given that $PR$ bisects $\angle QPR$, the measure of $\angle QPR$ is $64^\circ$, and the measure of $\angle RPS$ is $(2x + 10)^\circ$. We need to f

1. **State the problem:** We are given that $PR$ bisects $\angle QPR$, the measure of $\angle QPR$ is $64^\circ$, and the measure of $\angle RPS$ is $(2x + 10)^\circ$. We need to f

1. **Stating the problem:** We want to understand the quick formulas (rumus cepat) for geometric transformations. 2. **Types of geometric transformations:** The main types are tran

1. **State the problem:** We have a kite with vertices $K(0,2)$, $I(2,4)$, $T(4,2)$, and $E(2,0)$. We will perform three transformations: reflection across the y-axis, rotation $90

1. **State the problem:** Find the value of the missing angle $x$ in each triangle given two angles. 2. **Formula used:** The sum of the interior angles of a triangle is always $18

1. **State the problem:** Calculate the surface area of a rhombicuboctahedron with 18 square faces each of edge length 24 inches, and 8 triangular faces each with height approximat

1. **State the problem:** We are given two congruent triangles with side markings indicating corresponding sides. One triangle has an angle of $83^\circ$ and we need to find the va

1. **State the problem:** We are given two congruent triangles with corresponding sides marked by ticks and one angle marked $83^\circ$ in the first triangle. We need to find the v

1. **State the problem:** We have two circles touching externally. Circle A has equation $x^2 + y^2 - 2x - 2y = 4$ and circle B has equation $(x - a)^2 + (y - 14)^2 = 100$. We need

1. **Problem Statement:**\nWe are given rays $\overrightarrow{AB}$ and $\overrightarrow{BA}$ and segment $\overline{AB}$. We need to find the union and intersection of these sets o

1. **State the problem:** We need to verify that the measures of angles add up to $90$ degrees because it is a right angle. 2. **Important rule:** A right angle measures exactly $9

1. **State the problem:** We are given two angles, $\angle 1$ and $\angle 2$, with measures expressed in terms of $x$: $$\angle 1 = (x - 9)^\circ$$

1. **State the problem:** We need to find the new coordinates of point $M(2, -4)$ after a 90 degree clockwise rotation and then a translation up 2 units. 2. **Rotation formula:** A

1. **State the problem:** We have a triangle $L\!M\!N$ in the top-left quadrant and its image $L''\!M''\!N''$ in the bottom-right quadrant. We need to find the translation rule tha