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Basic Geometry

Basic Geometry

Similar Figures Examples

Example 1

Quadrilaterals ABCD and EFGH are congruent (ABCD ≅ EFGH). Find the measure of each missing angle and side.

ABCD and EFGH quadrilaterals

Example 2

Triangles ABC and DEF are similar (ABC ~ DEF). What is the length of side DF?

Similar Triangles ABC and DEF

Example 3

The sun casts a shadow on two trees in a field. The smaller of the two is 10.5 ft high and has a shadow 11.25 ft long. The shadow of the taller tree is 17.5 ft long. How tall is that tree?


This is actually how the heights of many tall structures are estimated!

Example 4

Pentagons OPQRS and TUVWX are both regular. Find the length of the apothem of TUVWX.


The apothem is the distance from the center of a regular polygon to the midpoint of one side.