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RHS Criteria for Congruency

Let ABC be a ...

Question

Let ABC be a triangle. Let D,E,F be points respectively on segments BC,CA,AB such that AD , BC, CF concurrent at point K . Suppose BD/DC = BF/FA and angle ADB= angle AFC. Prove that angle ABE = angle CAD

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A B C

be a triangle. Let

D, E, F

be the points respectively on the segments

B C, C A, A B

A D, B E, C F

concur at the point

K .

\frac{B D}{D C} = \frac{B F}{F A}

∠ A D B = ∠ A F C

∠ A B E = ∠ C A D . ?

A B C

be a triangle. Let

B E

C F

be internal angle bisectors of

∠ B

∠ C

, respectively, with

E

A C

F

A B .

X

is a point on the segment

C F

A X ⊥ C F

Y

is a point on the segment

B E

A Y ⊥ B E

X Y = \frac{(b + c - a)}{2}

B C = a

C A = b

A B = c

A B C

be an acute-angled triangle triangle, and let

D, E, F

B C, C A, A B

respectively such that

A D

B E

is the internal angle bisector and

C F

is the altitude. Suppose

∠ F D E = ∠ C, ∠ D E F = ∠ A a n d ∠ E F D = ∠ B

A B C

is equilateral.

D, E, F

be points on the sides

B C, C A, A B,

respectively, of a triangle

A B C

B D = C E = A F

∠ B D F = ∠ C E D = ∠ A F E

Δ A B C

is equilateral.

Q. Let ABC be an acute angled triangle in which D, E, F are points on BC, CA, AB respectively such that AD

⊥

BC, AE=EC and CF bisects

∠

C internally. Suppose CF meets AB and DE in M and N respectively. If FM

= 2

= 1

= 3

, Find the perimeter of the triangle ABC.

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