Answered: Prove that given two triangles ΔABC and…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Prove that given two triangles ΔABC and ΔDEF such that AC≅DF, ∢A≅∢D and ∢B≅∢E then ΔABC≅∆DEF, justifying the following steps:

a) Suppose that AB≇DE.

b) So DE<AB or AB<DE.

c) If DE<AB then there exists a point G between A and B such that AG≅DE.

d) Then ΔCAG≅∆FDE.

e) So ∢AGC≅∢E.

f) Then ∢AGC≅∢B.

g) This is a contradiction.

h) So DE is not less than AB.

i) A similar argument applies for a point H between DE such that AB≅DH.

j) Then ED≅AB.

k) Therefore ΔABC≅∆DEF

Please be as clear as possible, use definitions if necessary, explain in detail all the steps. Thak you a lot

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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