Two geometric figures are congruent when their corresponding dimensions and angles are identical, denoted by . We test congruence practically by placing paper cut-out shapes over each other. If a figure slides or rotates smoothly onto another without lifting off the flat surface or turning face down, both figures exhibit direct congruence. The shapes maintain matching orientations and identical corresponding measurements throughout the planar movement. Use Figure 1 to see how sliding a shape preserves its orientation.
- Congruent figures have identical side lengths, angle measures, and total area in plane geometry.
- The symbol denotes congruence between geometric shapes having equal corresponding dimensions.
- Direct congruence occurs when one shape superimposes onto another through translation or rotation alone.
- Paper cut-outs demonstrate direct congruence when aligned without flipping either shape face down.
Check question: A right-angled triangle with sides 5 cm, 12 cm, and 13 cm is rotated 180° about one of its vertices. Which of the following correctly classifies the congruence between the image and the original triangle?
- Direct congruence, because a rotation occurs within the plane without flipping the shape over.
- Opposite congruence, because a 180° rotation reverses the orientation of the triangle's vertices.
- Opposite congruence, because turning the shape upside down means it has been flipped face down.
- Direct congruence, because all geometric transformations result in directly congruent images.
Show answer
Direct congruence, because a rotation occurs within the plane without flipping the shape over. A 180° rotation spins the triangle within the flat plane. Because the shape is never lifted and flipped face down, its vertex orientation is preserved. Transformations that preserve orientation, such as rotations and translations, always produce direct congruence.
