Magic of Similar Quadrilaterals (investigation)
Context
I was messing about with similar quadrilaterals after reading one of my students, Dakota's, blogpost, and it turned into a pretty cool deformation of the plane.
Should lead to some cool tessellations, eh?
The tool two stage constructs 2 similar quadrilaterals on three sides of four given vertices.
Similar quadrilaterals are quadrilaterals that have the same shape but not necessarily the same size. This means their corresponding angles are congruent (equal in measure), and their corresponding sides are proportional (have the same ratio).
Similar Quadrilaterals
Analyze the text and investigate to answer the questions given:
Quadrilaterals ABCD and EFGH have three corresponding congruent angles: i) m(∠A)=m(∠E) ii) m(∠B)=m(∠F) iii) m(∠C)=m(∠G) a) Must it be true that m(∠D)=m(∠H)? Explain.
b) If ABCD and EFGH are isosceles trapezoids, are they always similar?
c) If ABCD and EFGH are rhombuses, are they always similar?