in triangles ABC and DEF, angle B = angle E, Angle F =angle C and AB 3de. then show that the two triangles are similar but not congruent
Answers
Step-by-step explanation:
to be congruent, the conditions are
S S S - three sides
S A S - two sides and the included angle
A S A - two angles and one side
R H S - R H S - Right angle, Htpotenuse and one side
But to be similar,
A A A means 3 angles
A A means only two angles ....
in both triangles should be equal.
In the problem, equality of two angles is given, but equality of sides is not given.
So, guven triangles are not congruent.
But they are similar.
Given : Triangle ABC and DEF <B = <E, <F= <C
AB = 3DE
To Find : correct option
congruent but not similar
similar but not congruent
neither similar nor congruent
none of these
Solution:
ΔABC & ΔDEF
∠B = ∠E
∠C = ∠F
=> ΔABC ≈ ΔDEF ( AA )
AB/DE = BC/EF = AC/DF
AB = 3DE
=> AB/DE = 3
=> AB/DE = BC/EF = AC/DF = 3
for triangles to be congruent side ratios must be 1
Triangles are similar but not congruent
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