1.4
Geometry
July 17, 2025
Shivohm Karogal
3
Min Read
AI Summary
These notes review key geometric concepts including congruence, similarity, and distance, with a focus on transformations such as reflection, translation, and rotation. They also explain how dilation shows similarity, how to estimate angles using triangle types, and how the Pythagorean Theorem helps compute distances in right-angled and compound shapes.
Objective
Understand congruence, similarity, and distance through transformations and formulas.
Core Concept
Congruence involves exact shape and size.
Similarity involves proportional scaling.
The Pythagorean theorem helps find distances.
Verifying Congruence via Transformations
Reflection: Flip the shape across a line.
Translation: Slide the shape without rotating.
Rotation: Turn the shape around a fixed point.
If all parts line up, the shapes are congruent.
Understanding Similarity via Dilations
Similar shapes have proportional sides and equal angles.
Dilation is resizing a shape by a scale factor while maintaining angle measures.
Using Congruence to Estimate Angles
For accurate angle estimation, check if triangles are:
Equilateral (all angles = 60°)
Isosceles (two angles equal)
Similar (scaling of one triangle to another)
Applying Pythagoras' Theorem to Compute Distances
Formula:
a² + b² = c²
Use to find missing sides in right-angled triangles.
Can be applied in compound shapes like rectangles containing diagonal lines or hidden triangles.