How To Solve: Similar Triangles
Attached pdf of this Article as SPOILER at the top! Happy learning! Hi All,
I have recently uploaded a video on YouTube to discuss
Similar Triangles in Detail:
Following is covered in the video
¤ Definition of Similar Triangles
¤ Properties of Similar Triangles
¤ Relationship of Perimeter of two Similar Triangles
¤ Relationship of Area of two Similar Triangles
Definition of Similar TrianglesTwo triangles are similar if at least two of their corresponding angles are equal.=> If two angles are equal then the third angle will also be equal (As sum of the angles is 180°)
=> If all three corresponding angles of two triangles are equal then they are similar triangles
Image-1.jpg (10.69 KiB) Viewed 319 times
Open
In above Figure △ ABC and △ DEF are similar because ∠A = ∠D, ∠B = ∠E and ∠C = ∠F
Properties of Similar TrianglesIf two triangles are similar, then their corresponding sides will be in the same ratio.
Image-1.jpg (10.69 KiB) Viewed 319 times
Open
In above Figure △ ABC and △ DEF are similar
=>
=
=
Relationship of Perimeter of two Similar TrianglesRatio of Perimeter of two similar triangles is equal to the ratio of their sides.
Image-1.jpg (10.69 KiB) Viewed 319 times
Open
In above Figure △ ABC and △ DEF are similar
=>
=
=
= k (assume)
=> AB = k*DE
=> BC = k*EF
=> AC = k*DF
=> Perimeter of △ ABC / Perimeter of △ DEF =
=
=
= k =
=
=
Relationship of Area of two Similar TrianglesRatio of Area of two similar triangles is equal to square of ratio of their sides.
Image-2.jpg (11.85 KiB) Viewed 301 times
Open
In above Figure △ ABC and △ DEF are similar and AG is perpendicular(⊥) to BC and DH ⊥ EF
If we consider △ AGB and △ DHE, then ∠B = ∠E, ∠G = ∠H = 90° => ∠GAB = ∠HDE
=> △ AGB and △ DHE
=> Their sides will be in the same ratio
=>
=
=
...(1)
And we already know that △ ABC and △ DEF
=>
=
=
= k ...(2)
From (1) and (2) we get
=
=
=
=
=
= k
=> Area of △ ABC / Area of △ DEF = (
* BC * AG) / (
* EF * DH) =
=
*
= k * k =
Hope it helps!
Good Luck!