📐 geometry

1. The problem asks to find the distance between the points $(15,11)$ and $(33,36)$. 2. We use the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$:

1. **Stating the problem:** We have two points describing a mountain climbing expedition: Point A at (11,200 meters east, 3,200 meters above base camp) and Point B at (8,400 meters

1. **State the problem:** We are given two angles formed by a transversal crossing two parallel lines. The angles are \( (85 - 2x)^\circ \) and \( (93 - 4x)^\circ \). We need to so

1. **State the problem:** We need to find the measure of angle $\angle RTN$ given two expressions for angles formed by two parallel lines cut by a transversal: one angle is $(55 -

1. **State the problem:** Find the area of the compound figure composed of rectangles and triangles with given side lengths. 2. **Analyze the figure:** The figure can be divided in

1. **State the problem:** We have a right triangle with one leg measuring 132 cm and the hypotenuse measuring 165 cm. We need to find the length of the other leg. 2. **Formula used

1. The problem asks to identify the highlighted part of circle O, where O is the center of the circle and the shaded region is between points O and S. 2. In circle geometry, a **se

1. The problem asks to identify the highlighted part of circle O. 2. Important definitions:

1. **Problem statement:** Given that \(\overline{AD} \parallel \overline{EG}\), \(\overline{BH} \perp \overline{FC}\), and \(m\angle ABH = 149^\circ\), find \(m\angle EFH\). 2. **I

1. **State the problem:** We have a right triangle with one leg $x$, another leg 25 cm, and an angle of 48° opposite the 25 cm side. We need to find the length $x$ to the nearest c

1. **Problem Statement:** We have two bearings from the north direction: 135° and 060°, with distances 8 km and 15 km respectively. We want to find the relative position of the two

1. The problem asks to find the measure of segment AC. 2. To solve this, we need more information such as the length of AC or other related segments, or a figure with points A, B,

1. **Stating the problem:** We have a right-angled quadrilateral with given side lengths and an angle of 130° at point C. We need to find all missing measures, including side lengt

1. **Problem statement:** Given rhombus ABCD with \(\angle ADC = 64^\circ\) and equilateral triangle BCE, find \(\angle CAE\). 2. **Properties and formulas:**

1. The problem is to understand and apply CPCTC (Corresponding Parts of Congruent Triangles are Congruent). 2. CPCTC is used after proving two triangles are congruent by methods li

1. **State the problem:** Given that $\overline{CA} \cong \overline{CE}$ and $\overline{BA} \cong \overline{DE}$, prove that $\overline{BX} \cong \overline{DX}$. 2. **Identify know

1. **State the problem:** We need to find the total length of 12 vertical support beams on a bridge. There are 6 beams on each side, evenly spaced along the length of the bridge. 2

1. **State the problem:** Dilate figure PQRS by a scale factor of $\frac{1}{2}$ with the center of dilation at point P.

1. The problem asks to identify which pair of angles are alternate interior angles when two parallel lines are cut by a transversal. 2. **Definition:** Alternate interior angles ar

1. The problem asks to identify which angle is the alternate interior angle to angle 1 when three parallel lines are cut by a transversal. 2. Alternate interior angles are pairs of

1. **Problem statement:** An equilateral triangle is inscribed in a circle of radius 10 cm. Find the area of the triangle. 2. **Formula and important rules:**