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Q.

The base BC of is produced on both sides of it upto points D and E. If $∠ A B D$ is greater than $∠ A C E$ , then which of the following is not true?

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a

∠ A B C

is smaller than

∠ A C B

.

b

AC is greater than AB.

c

AB is greater than AC.

d

A B + A C > B C

answer is B.

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Detailed Solution

In option 1, we have

∠ A B D > ∠ A C E

. It is true. So,

(180 ∘ − ∠ A B D) < (180 ∘ − ∠ A C E) ∠ A B C < ∠ A C B

We are aware that if two angles of a triangle are equal, then its two opposite sides will also be equal. Similarly, we can apply this idea here. We already know that angle ABC is less than angle ACB.
Consequently, side AC is less than side AB. So side AC is less than side AB.
Consequently, the statement in option 2 contradicts this condition.
So the correct option is 2.

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The base BC of is produced on both sides of it upto points D and E. If ∠ABD is greater than ∠ACE , then which of the following is not true?