Fill the blanks in the following so that each of the following statements is true.
(i) Sides opposite to equal angles of a triangle are ......
(ii) Angle opposite to equal sides of a triangle are .....
(iii) In an equilateral triangle all angles are .....
(iv) In a ΔABC if ∠A = ∠C , then AB = ......
(v) If altitudes CE and BF of a triangle ABC are equal, then AB = ....
(vi) In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
(vii) In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……

Explanation

(i) Sides opposite to equal angles of a triangle are equal.
(ii) Angles opposite to equal sides of a triangle are equal.
(iii) In an equilateral triangle all angles are equal.
Reason: Since all sides are equal in an equilateral triangle, the angles opposite to equal sides will be equal.
(iv) In `/_\ABC` if `/_A =/_C`, then `AB =BC`.
Reason: Since the sides opposite to equal angles are equal, the side opposite to `/_A`
`=>BC` and `/_C`
`=>AB` are equal.
(v) If altitudes `CE` and `BF` of a triangle `ABC` are equal, then `AB =AC`.
Reason: From `RHS` congruence criterion:
/_\BEC~=/_\CFB
/_EBC=/_FCB
=>/_ABC = /_ACB
AC=AB [ since, Sides opposite to equal angels are equal]
(vi) In an isosceles triangle `ABC` with `AB = AC`, if `BD` and `CE` are its altitudes, then `BD` is equal to `CE`
Reason: Since angles opposite to equal sides are equal.
So, by `ASA` congruence criterion [Corresponding parts of congruent triangles are equal]
(vii) In right triangles `ABC` and `DEF`, if hypotenuse `AB=EF` and side `AC=DE`, then. `/_\ABC~=/_\EFD`
Reason: From the `RHS` congruence criterion we have :
`/_\ABC~=/_\EFD`