Constructing an Isosceles Triangle with Mirror Symmetry (Q5)

This example demonstrates how an isosceles triangle’s key geometric relationships can be built dynamically in the coordinate plane using symmetry. It emphasizes congruence reasoning: corresponding sides and angles are enforced through construction steps, while mirror transformations and angle/circle constraints guide the configuration. The core mathematics includes isosceles-triangle properties, congruence ideas, coordinate-geometry relationships between points and segments, and geometric constraints using angles and circles. In GeoGebra, the construction uses Textfield/InputBox-style parameter inputs, Polygon to form the triangle, Segment to connect defining points, Angle to measure/control the relevant angle(s), Circle to generate constraint loci, Point to create the dependent construction points, If to switch between conditional construction branches, Mirror to reflect points across a symmetry axis/line, and Intersect to compute intersection points that determine the final geometry. Suitable for middle/high-school geometry lessons, especially when teaching congruence, symmetry, and dynamic construction with GeoGebra.