Question

10. In the adjoining figure, CD is an altitude of AABC. DE and
DF are perpendiculars from D on the sides AC and BC
respectively such that DE = DF. Show that ADEC and ADFC
are congruent.
A
D
B​

Answer 1

Answer:

• In triangle ABC
• D is the midpoint of BC
• DE perpendicular to AB
• And DF perpendicular to AC
• DE=DF

To prove:

• Triangle ABC is an isosceles triangle  

Proof:

• In the right angles triangle BED and CDF
• Hypotenuse BD=DC ( because D is a midpoint )
• Side DF=DE ( given)
• △BED≅CDF ( RHS axiom)
• ∠C=∠B
• AB=AC ( sides opposite to equal angles
• △ABC is an isosceles triangle