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Altitude of a Triangle and Drawing Method

Draw a diagra...

Question

Draw a diagram for the following statements and prove that result :
Any two altitudes of an equilateral triangle are congruent.

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Solution

$\begin{matrix} A B = B C = C A \Rightarrow ∠ A = ∠ B = ∠ c \Rightarrow A D b i s e c t B C i n e q u a l p a r t a n d B E a l s o b i sec t A C i n t o t w o e q u a l p a r t s \Rightarrow Δ A D C ≃ Δ B E C, b y S . A . S c r i t e r i a . H e n c e, B E a n d A D a r e c o n g r u e n t A n s . \end{matrix}$

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Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent.

(i) Two equilateral triangles are similar.

(ii) If angles in a linear pair are congruent then each of them is a right angle.

(iii) If the altitudes drawn on two sides of a triangle are congruent then those two sides are congruent.

Q. Draw a diagram for the following statements and prove that result :
In an isosceles triangle, the median joining the vertex (formed by intersection of equal sides) to the midpoint of opposite side is also an altitude.

Q. Select the correct statement for the following:

A

: The angles of an equilateral triangle are equal.

B

: Angles opposite to two congruent sides of a triangle are congruent.

Q. BE and CF, the altitudes of

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ABC are equal. Prove that

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ABC is an equilateral triangle.

Q. AD,BE and CF, the altitudes of triangle ABC are equal. Prove that triangle ABC is an equilateral triangle.

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Altitude of a Triangle and Drawing Method

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