Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below to enlarge it.
Draw circle centered A, radius=ADLocate point H on the circle such that ∠ (HAF)= ∠ (DAF)= alphaTriangles FAD congruence to HAF ( Case SAS) => FH=FD= b and ∠(AHF)=90We have ∠ (EAH)=45- alpha=∠ (BAE) => triangles EAH congruence to EABSo EH=EB=a and ∠ (EHA) 90So x= a+b
Rotate anti-clockwise 90°, center at A. Then D→B. Let F→G. Then AF=AG and ∠EAF=∠EAG. So ΔEAF congruent to ΔEAG. Hence, x=EF=EG=a+b.
Fold AB, AD along AE, AF respectively.B, D land at the same point P on EF. So x = EP + PF = EB + DF = a + b.
Extend CD to G such that DG = a, then Tr.s ABE and ADG are congruent from which we can deduce that Tr.s AFE and AGF are also congruent. Hence x= FG = a+bSumith PeirisMoratuwa Sri Lanka