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RHS Criteria for Congruency

In Δ A B C ...

Question

In $Δ A B C$ $B E$ and $C F$ are the two equal altitudes. Prove $Δ A B C$ is isoceles by R.H.S

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Solution

$\begin{matrix} G i v e n ∠ A E B = ∠ C E B = 90^{\circ} - - - - (1) A l s o, C F i s a a l t i t u d e, S o, ∠ A F C = ∠ B F C = 90^{\circ} - - - (2) A l s o, B E = C F - - - (3) W e h a v e t o p r o v e t h a t Δ A B C i s i s o c e l e s . I n Δ B C F a n d Δ C B E ∠ B F C = ∠ C E B = 90^{\circ} F C = E B (f r o m 3) B C = C B (c o m m o n) ∴ Δ B C F ≅ Δ C B E b y R H S c o n g r u e n c e r u l e ∴ ∠ F B C = ∠ E C B s o, ∠ A B C = ∠ A C B A B = A C H e n c e, Δ A B C i s a n i s o s c e l e s t r i a n g l e . \end{matrix}$

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Similar questions

Q. AD, BE and CF, the altitudes of

Δ A B C

are equal. Prove that

Δ A B C

is an equilateral triangle

Q. The altitudes of

Δ A B C

, AD, BE and CF are equal. Prove that

Δ A B C

is an equilateral triangle.

B E

C F

are two equal altitudes of

Δ A B C

. By using RHS congruency rule, prove that

Δ A B C

is an isosceles triangle.

A D, B E

C F

, the altitude of

Δ A B C

are equal. Then

Δ A B C,

A D, B E

C F

are the altitudes. If

A B \times A C = 28.80

B E \times C F = 20,

A D \times B C

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