If the altitudes from two vertices of a triangle to the opposite sides are equal then the triangle is

(a) equilateral (b) isosceles

(c) scalene (d) right angled

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Solution

ANSWER:
(b) isosceles
In ∆ABC, BL∥AC.
CM∥AB such that BL=CM.
To prove: AB = AC
In △ABL and △ACM,BL=CM
∴ AB=AC (CPCT)

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Q. Question 8
The points (-4,0), (4,0) and (0,3) are the vertices of a
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Which of the following statements are true (T) and which are false (F):

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(ii) Angles opposite to equal sides of a triangle are equal.

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(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

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If the altitudes from two vertices of a triangle to the opposite sides are equal then the triangle is (a) equilateral (b) isosceles (c) scalene (d) right angled

ANSWER: (b) isosceles In ∆ABC, BL∥AC. CM∥AB such that BL=CM. To prove: AB = AC In △ABL and △ACM,BL=CM ∴ AB=AC (CPCT)

If the altitudes from two vertices of a triangle to the opposite sides are equal then the triangle is

(a) equilateral (b) isosceles

(c) scalene (d) right angled

ANSWER:
(b) isosceles
In ∆ABC, BL∥AC.
CM∥AB such that BL=CM.
To prove: AB = AC
In △ABL and △ACM,BL=CM
∴ AB=AC (CPCT)