📐 geometry

1. **State the problem:** We need to use the parallelogram side theorem and ASA (Angle-Side-Angle) congruence to find congruent triangles in a parallelogram and show that its diago

1. **Problem Statement:** Given two triangles ABC and A'B'C' on concurrent lines L, M, N meeting at point O, with AB \parallel A'B' and BC \parallel B'C', use Thales theorem to sho

1. **Problem Statement:** Given points A, B, C, A', B', C' on concurrent lines L, M, N meeting at point O, with AB \parallel A'B' and BC \parallel B'C', prove using Thales' theorem

1. **State the problem:** Find the area of the colored part of the figure in problem 3, which is a heart shape with a dimension labeled 5 cm.

1. The problem asks to find the value of angle $b$ in a triangle where two angles are given: $38^\circ$ and $101^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the in

1. **State the problem:** We have a circle with a secant line FED and a tangent line CD. Given the lengths CD = 43 and ED = 31, we need to find the length of FE. 2. **Recall the ta

1. **Énoncé du problème :** Soit un triangle FAL. On définit les points I, J, K par :

1. Masalah: Tentukan koordinat bayangan segitiga ABC dengan koordinat A(2,1), B(5,-1), dan C(4,3) oleh pencerminan terhadap sumbu Y (soal b). 2. Rumus pencerminan terhadap sumbu Y:

1. The problem involves a right triangle ABC with right angle at C, hypotenuse AB, and altitude CD drawn perpendicular to AB at D. 2. We are given three parts:

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