Question

Show that the diagonals of a rhombus divide it into four congruent triangles.

Answer 1

Answer:

diagonals of a rhombus divide it into four congruent triangles.

Step-by-step explanation:

let say rhombus KITE

Let say Length of Diagonals KT = 2a & IE = 2b

as we know that Diagonal of rhombus perpendicularly bisect each other

Let say intersection point = O

then KO = OT = 2a/2 = a

& IO = OE = 2b/2 = b

now ΔKOI  , ΔIOT , ΔTOE , ΔEOI

KO = a , OI = b ∠KOI = 90°

OT = a   IO = b  ∠IOT = 90°

OT = a   OE = b  ∠TOE = 90°

OI = a    OE = b  ∠EOI = 90°

All four triangles have two sides equal and angle between them Equal

so all four triangles are congruent