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Converse of Basic Proportionality Theorem

Question 4 iA...

Question

Question 4 (i)
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
(i) $Δ A B E ≅ Δ A C F$

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Solution

$I n Δ A E B a n d Δ A F C, W e h a v e ∠ A = ∠ A (C o m m o n a n g l e) B E = C F (G i v e n) ∠ B E A = ∠ C F A (E a c h e q u a l t o 90^{\circ}) T h e r e f o r e, b y A A S r u l e, Δ A E B ≅ Δ A F C$

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Similar questions

Q. Question 4 (i)
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
(i)

Δ A B E ≅ Δ A C F

Q. Question 4 (ii)
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
AB = AC,

i . e . Δ A B C i s a n i s o s c e l e s t r i a n g l e .

Q. Question 4 (ii)
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
AB = AC,

i . e . Δ A B C i s a n i s o s c e l e s t r i a n g l e .

Q. Question 3
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

Q. Question 3
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

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Converse of Basic Proportionality Theorem

Standard X Mathematics

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