Step 1
To make the triangle congruent by using the SAS congruence,
First naming the edges and vertex of the triangle,
Step 2
By using sum of interior angle property in \(\displaystyle\triangle{A}{B}{C}{\quad\text{and}\quad}\triangle{D}{E}{F}\),
\(\displaystyle\angle{A}{B}{C}={180}^{{\circ}}-{\left(\angle{A}{B}{C}+\angle{B}{A}{C}\right)}\)
\(\displaystyle\angle{D}{E}{F}={180}^{{\circ}}-{\left(\angle{E}{D}{F}+\angle{D}{F}{E}\right)}\)
it is given that,
\(\displaystyle\angle{A}{C}{B}=\angle{E}{D}{F}={90}^{{\circ}}\) (given)...(i)
\(\displaystyle\angle{B}{A}{C}=\angle{D}{F}{E}{\left({g}{i}{v}{e}{n}\right)}\)...(ii)
Adding equation (i) and (ii) and subtracting them form \(\displaystyle{180}^{{\circ}}\) in both sides,
\(\displaystyle{180}^{{\circ}}-{\left(\angle{A}{C}{B}+\angle{B}{A}{C}\right)}={180}^{{\circ}}-{\left(\angle{E}{D}{F}+\angle{D}{F}{E}\right)}\)
\(\displaystyle\angle{A}{B}{C}=\angle{D}{E}{F}\)
Now, in \(\displaystyle\triangle{A}{B}{C}{\quad\text{and}\quad}\triangle{D}{E}{F}\),
AB=EF(given)
\(\displaystyle\angle{A}{B}{C}=\angle{D}{E}{F}\)(Proved above)
BC=DE(given)
\(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{D}{E}{F}\) (By SAS Congruence Theorem)
Yes, the provided information is enough to prove the triangle congruent by SAS.
Question
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.12210203322.jpg
Answers (1)
2020-12-17
Relevant Questions
asked 2021-02-13
decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.
asked 2021-07-22
To decide: Whether the given information is enough to prove that \(\displaystyle\triangle{W}{X}{Z}\stackrel{\sim}{=}\triangle{Y}{Z}{X}\) using SAS Congruency Theorem. If so write a proof if not then explain the reason.
Given:
The given figure is as follows.
Given:
The given figure is as follows.
asked 2021-03-09
What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?
A)\(\displaystyle\angle{B}{A}{C}\stackrel{\sim}{=}\angle{D}{A}{C}\)
B)\(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}\)
C)\(\displaystyle\angle{B}{C}{A}\stackrel{\sim}{=}\angle{D}{C}{A}\)
D)\(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{B}{D}}}\)
asked 2020-11-05
Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not. write no congruence can be deduced.
