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Which of the following statements is/are true? A: In a scalene ΔPQR, A and B are the mid points of PQ and PR respectively, then ∠BAQ is equal to ∠ABR. B: In a scalene ΔABC, if AD is perpendicular to BC, then ΔADB and ΔADC will be similar to each other. C: The number of diagonals cannot be less than one in a polygon.

Which of the following statements is/are true? A: In a scalene ΔPQR, A and B are the mid points of PQ and PR respectively, then ∠BAQ is equal to ∠ABR. B: In a scalene ΔABC, if AD is perpendicular to BC, then ΔADB and ΔADC will be similar to each other. C: The number of diagonals cannot be less than one in a polygon. Correct Answer None

CONCEPT:

Properties of triangle, similarity, and congruency

CALCULATION:

A:

In a scalene ΔABC, AD is perpendicular to BC.

In both the triangles ΔADB and ΔADC, only ∠ADB = ∠ADC and AD is common side, but no other angles or side are equal. So, ΔADB and ΔADC are not similar.

C: The number of diagonals cannot be less than 1 in a polygon.

The number of diagonals in a triangle = /2 = 3 × (3 – 3)/2 = 0

Hence, none of the statement is true.

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