Question

For the triangles shown, we can express their congruence with the statement /_ABC ~= /_FED. By reordering the vertices, express this congruence with a different statement. 12210203302.jpg

Congruence
ANSWERED
asked 2020-12-09
For the triangles shown, we can express their congruence with the statement \(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{F}{E}{D}\). By reordering the vertices, express this congruence with a different statement.
image

Answers (1)

2020-12-10
Step 1
Given- The triangles ABC and FED are congruence with \(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{F}{E}{D}\) from the given figure,
image
To express- The congruence with a different statement by reordering the vertices.
Concept Used- Two triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any orientation.
Step 2
Explanation- As we know that two triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any orientation.
Now, from the figure, as we see that the corresponding sides and corresponding angles are equal, so using the congruence law , we can write in correct order as,
\(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}{F}{E}{D}\).
So, the correct order of congruence can be written as \(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}{F}{E}{D}\).
Answer- Hence, the congruence with a different statement by reordering the vertices can be writtena as \(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}{F}{E}{D}\).
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