Math

Solution of triangles

In ABC and AGHI below, ZA is congruent to ZG and Z8 is congruent to ZH.
C
H
Complete the paragraph to prove that AABC - AGHI.
Since AB and GH are corresponding sides, first dilate ABC about A with scale factor
to get AAB'C'. Next, translate and rotate AAB'C' to get AA'B"C" where A' coincides
with Gand A'Bcoincides
Since A'B" =
, this means B" coincides with
Since dilations, translations, and rotations preserve angle measure,
and
ZB" - ZH. This means A'Ccoincides with GÌ and
coincides with HT. Both C" and
are at the
- of GÌ and H1, so C" coincides with I. Therefore, AA'B"C" coincide
with AGHI. This means ABC can be mapped onto AGHI by a sequence of
SO AABC ~ AGHI.