if two right angled triangle which side are equal to hypotenuse and one side of triangle so that they are equal
Answers
Step-by-step explanation:
Both the hypotenuse of the triangles are equal
One of other two sides are equal
Both are right angled triangles.
So by Side Angle Side we can say that both the angles are congruent........
Step-by-step explanation:
answr
search
What would you like to ask?
7th
Maths
Congruence of Triangles
Criteria for Triangle Congruence
If in two right triangles t...
MATHS
If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then prove that two triangles are congruent.
MEDIUM
Share
Study later
ANSWER
Given:Two right triangles △ABC and △DEF where ∠B=90
∘
and ∠E=90
∘
, hypotenuse is equal.
i.e., AC=DF and one side is equal i.e.,BC=EF
To prove:△ABC≅△DEF
Proof:In right △ABC
By pythagoras theorem, AC
2
=AB
2
+BC
2
AB
2
=AC
2
−BC
2
........(1)
In right △DEF
By pythagoras theorem, DF
2
=DE
2
+EF
2
DE
2
=DF
2
−EF
2
........(2)
From (1)
AB
2
=AC
2
−BC
2
⇒AB
2
=DF
2
−EF
2
since AC=DF and BC=EF
⇒AB
2
=DE
2
from (2)
⇒AB=DE ......(3)
Given:BC=EF,AC=DF
⇒△ABC≅△DEF by SSS congruence.
Hence proved.