📐 geometry

1. The problem asks to find the unknown angle $x^\circ$ in the given figure with two right triangles adjacent to each other. 2. Important information: The left triangle is an isosc

1. **State the problem:** Points A, B, and C are collinear with B between A and C. Given $AB = 12$ and $AC = 19$, find $BC$. 2. **Formula and rule:** When three points are collinea

1. **Problem statement:** We have a sequence of transformations: a translation, a reflection over line $\overleftrightarrow{PQ}$, and a reflection over line $\overleftrightarrow{RS

1. **Problem statement:** We are given triangle ABC with angle bisector AD, where \(\angle DAC = \angle BAD\). We need to find the length of segment \(\overline{BD}\) given \(AC =

1. Problem: Find the image coordinates of points P(6, -2), Q(-9, -3), and R(-2, 5) after translations: a) by T(5, 1)

1. **Problem statement:** We are given two triangles, \(\triangle ARS\) and \(\triangle EST\), sharing point \(S\). Segments \(\overline{RA}\) and \(\overline{ET}\) are parallel. W

1. **Problem statement:** We are given a triangle WLY with a point A on side LW. Segment LW is unknown, segment AY is 7 units, and segment AL is 3.5 units. Angles AYL and AYW are r

1. **Problem statement:** We are given a triangle WLY with a point A on side LW. Segment LW is unknown, segment AY is 7 units, and segment AL is 3.5 units. Angles AYL and AYW are r

1. **Problem statement:** We have two triangles, \(\triangle FOR\) and \(\triangle FAN\), where \(\overline{OR} \parallel \overline{AN}\). Given \(OR = 11.2\) units, \(FO = 7\) uni

1. **Problem statement:** We are given triangles BOX and DOP with right angles at \(\angle BXO\) and \(\angle ODP\). Point O lies between X and D on segment XD. Ray OL bisects \(\a

1. **Đề bài:** Cho tam giác ABC, điểm D chia đoạn BC theo tỉ số 1:2, điểm O chia đoạn AD theo tỉ số 3:2. Gọi K là giao điểm của BO và AC. Tính tỉ số $AK : KC$. 2. **Phân tích bài t

1. **State the problem:** We start at point A, travel 7 km on a bearing of 135° to point B, then from B travel 12 km on a bearing of 250° to point C. We need to find the distance a

1. **Problem statement:** Find the unknown angle $x$ in the given figure with two tangent circles and given angles $37^\circ$, $60^\circ$, and $80^\circ$. 2. **Understanding the fi

1. The problem is to determine which angle is congruent to \(\angle HUI\) from the given options: \(\angle GUI\), \(\angle IGU\), or \(\angle UIG\). 2. Congruent angles have the sa

1. The problem asks which pair of congruent corresponding parts is needed to prove that two triangles are congruent using the SAA (Side-Angle-Angle) congruence conjecture. 2. The S

1. **Stating the problem:** We are given six expressions involving variables $d$ and $b$:

1. **State the problem:** We have a swimming pool with an inside perimeter of 24 meters and an outside perimeter of 48 meters. We want to find how many stepping stones are needed t

1. **State the problem:** We are given triangle $\triangle ABC$ with sides $AB=0.9$, $BC=1$, and $AC=1.5$. We need to determine which of the given triangles $\triangle DEF$ or $\tr

1. **Stating the problem:** We are given a segment \(\overline{BD} = 12\) cm and points \(A, B, C, D, O\) on a figure. We need to find the length \(\overline{BO}\). 2. **Understand

1. **Problem statement:** Find the area of the shaded quarter circle inside a square with side length 7 cm. 2. **Formula used:** The area of a quarter circle is given by

1. **State the problem:** We need to find the perimeter of the blue shape drawn on a 7 by 7 grid where each square side measures 1 cm. 2. **Understand the perimeter:** The perimete