Question

Question for 25 points please answer.

Write the antecedent (given part) and the consequent (part to be proved) in the following
statements.

(1) If all sides of a triangle are congruent then its all angles are congruent.

(2) The diagonals of a parallelogram bisect each other.
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Answer 1

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Answer 2

Answer:

1) Since, AB, BC and AC have ∠A, ∠B and ∠C respective angles then accordingly, if the sides of the triangle are congruent then the angles corresponding to them are always congruent. Hence, ∠A≅∠B≅∠C which is the consequent part of the given statement.

2) ABCD is a parallelogram, diagonals AC and BD intersect at O.

In triangles AOD and COB,

DAO = BCO (alternate interior angles)

AD = CB.

ADO = CBO (alternate interior angles)

AOD COB (ASA)

Hence, AO = CO and OD = OB (c.p.c.t)

Thus, the diagonals of a parallelogram bisect each other.

Step-by-step explanation:

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