Mathematics
Show that the two triangles given in the following figure are congruent.
Triangles
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Answer
Given: BD = 28 cm
BC = 16 cm
CD = BD - BC = 28 - 16 = 12 cm
In Δ CDE, using Pythagoras theorem,
Hypotenuse2 = Base2 + Height2
⇒ CE2 = CD2 + DE2
⇒ (20)2 = (12)2 + DE2
⇒ 400 = 144 + DE2
⇒ DE2 = 400 - 144
⇒ DE2 = 256
⇒ DE = = 16
In Δ ABC, using Pythagoras theorem,
⇒ AC2 = AB2 + BC2
= (12)2 + (16)2
= 144 + 256
= 400
⇒ AC = = 20 cm
So, AB = CD, BC = DE and AC = CE.
Hence, the two triangles ABC and CDE are congruent.
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