Both the triangles of the given figure are similar to each other by SAS
( Side angle Side ) the property of corresponding sides are in proportion and included angle of both the triangles is right angle.
Slope of the both the triangles is (-3/2) .
As given in the question,
For the given diagram of the two triangles,
To prove : Both the triangles are similar to each other.
Side length of the corresponding sides of both the triangles :
Altitude of :
Small triangle : 6 - 3 = 3 units
Big triangle : 3 - (-3) = 6 units
Base :
Small triangle : -2 + 4 = 2 units
Big triangle : 2 - (-2) = 4 units
Corresponding sides are in proportion:
( 3/6) = 1/2 = ( 2 / 4)
And the included between the two sides is equal to 90° ( right angle ).
By SAS ( Side angle Side ) theorem,
Both the triangles are similar to each other.
Now slope of :
Small triangle is equal to,
Consider two end points ( -4, 6) and ( -2 , 3)
Slope = ( 3 -6)/ (-2 + 4)
= -3/2
Big triangle is equal to,
Consider two end points ( -2, 3) and ( 2 , -3)
Slope = ( -3 -3)/ ( 2 + 2)
= -6 /4
= -3/2
Therefore, both the triangles of the given figure are similar to each other by SAS
( Side angle Side ) the property of corresponding sides are in proportion and included angle of both the triangles is right angle.
Slope of the both the triangles is (-3/2) .
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