Math Problem Statement

Geometry problems involving triangle congruence, perpendicular lines, and parallel lines. Problem 1 features an isosceles triangle \(\triangle ABC\) with \(AB = AC\) and points \(M\) on \(AC\) and \(N\) on \(AB\) such that \(AM = AN\). Problem 2 involves points on the coordinate plane \((Oxy)\) with conditions on distances and line intersections.

Solution

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  • Bài 1 (B1) involves a triangle ΔABC\Delta ABC with AB=ACAB = AC, and points MM on segment ACAC and NN on segment ABAB, with the given condition AM=ANAM = AN.
  • Bài 2 (B2) involves another geometric scenario where points CC and DD lie on the OxyOxy plane, with conditions on the lengths OA=OCOA = OC and AB=CDAB = CD.

The problems require proving certain geometric properties and relationships like congruence, parallelism, and perpendicularity.

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Math Problem Analysis

Mathematical Concepts

Triangle congruence
Isosceles triangle properties
Line parallelism and perpendicularity
Coordinate geometry

Formulas

Distance formula in coordinate geometry
Triangle area formula
Slope formula for parallel and perpendicular lines

Theorems

Congruent triangles (SAS, ASA, and SSS)
Properties of isosceles triangles (equal sides and angles)
Parallel line theorem
Perpendicular line theorem

Suitable Grade Level

Grades 9-11