Question

Select all the true statements. 12210203832.jpg A./_\FGK ~= /_\FJK B./_GKH ~= JKH C.bar(FG) ~= bar(KG) D./_GFH ~= /_JFH E./_\GKH ~= /_\JKH F.bar(FG) ~= bar(JK)

Congruence
ANSWERED
asked 2020-10-23
Select all the true statements.
image
A.\(\displaystyle\triangle{F}{G}{K}\stackrel{\sim}{=}\triangle{F}{J}{K}\)
B.\(\displaystyle\angle{G}{K}{H}\stackrel{\sim}{=}{J}{K}{H}\)
C.\(\displaystyle\overline{{{F}{G}}}\stackrel{\sim}{=}\overline{{{K}{G}}}\)
D.\(\displaystyle\angle{G}{F}{H}\stackrel{\sim}{=}\angle{J}{F}{H}\)
E.\(\displaystyle\triangle{G}{K}{H}\stackrel{\sim}{=}\triangle{J}{K}{H}\)
F.\(\displaystyle\overline{{{F}{G}}}\stackrel{\sim}{=}\overline{{{J}{K}}}\)

Answers (1)

2020-10-24
Step 1
Given:
image
Step 2
We have,
\(\displaystyle{I}{n}\triangle{F}{G}{H}{\quad\text{and}\quad}\triangle{F}{J}{H}\),
FG=FJ(Given)
GH=JH(Given)
FH=FH(Common side)
So, by SSS congruence criteria
\(\displaystyle\triangle{F}{G}{H}\stackrel{\sim}{=}\triangle{F}{J}{H}\)...(i)
A.\(\displaystyle{I}{n}\triangle{F}{G}{K}{\quad\text{and}\quad}\triangle{F}{J}{K}\),
FG=FJ(Given)
\(\displaystyle\angle{G}{F}{K}=\angle{J}{F}{K}\) [Using(i)]
FK=FK(Common side)
So, by SAS congruence criteria
\(\displaystyle\triangle{F}{G}{K}\stackrel{\sim}{=}\triangle{F}{J}{K}\)
B.Similarity, using(i) and A, we get
\(\displaystyle{I}{n}\triangle{G}{K}{H}{\quad\text{and}\quad}\triangle{J}{K}{H}\),
GK=JK[Using(A)]
GH=JH(Given)
KH=KH(Common side)
So, by SSS congruence criteria
\(\displaystyle\triangle{G}{K}{H}\stackrel{\sim}{=}\triangle{J}{K}{H}\)
Hence, \(\displaystyle\angle{G}{K}{H}\stackrel{\sim}{=}\angle{J}{K}{H}\)
D.Using(i),\(\displaystyle\angle{G}{F}{H}\stackrel{\sim}{=}\angle{J}{F}{H}\)
E.Already proved in B, \(\displaystyle\triangle{G}{K}{H}\stackrel{\sim}{=}\triangle{J}{K}{H}\)
C & F. These two points are False.
Step 3
Hence the true statements are A, B, D, and E.
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