If $△ A B C$ and $△ D B C$ are on the same base BC,AB=DC and AC=DB,then which of the following gives a CORRECT congruence relationship?

△ A B C = △ D B C

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△ A B C = △ C B D

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△ A B C = △ D C B

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△ A B C = △ B C D

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Solution

The correct option is D $△ A B C = △ D C B$
In triangle $Δ A B C$ and $Δ D C B$ we have
$A B = D C$ , $A C = D B$ and $B C = B C$
then from $S S S$ congruence , $Δ A B C = Δ D C B$

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Question 49

If $Δ A B C$ and $Δ D B C$ are on the same base BC, AB = DC and AC = DB as shown in the figure, then which of the following gives a congruence relationship?

a) $Δ A B C ≅ Δ D B C$
b) $Δ A B C ≅ Δ C B D$
c) $Δ A B C ≅ Δ D C B$
d) $Δ A B C ≅ Δ B C D$

Two triangles ABC and DBC have common base BC. Suppose AB = DC and ∠ABC = ∠BCD. Prove that AC = BD.

Q. In the adjoining figure,

A B C

and

D B C

are two triangles on the same base

B C, A L ⊥ B C

and

D M ⊥ B C

. Then,

\frac{a r e a (△ A B C)}{a r e a (△ D B C)}

is equal to:

Q. Question 8
ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

Q. Triangle ABC and DBC are on the same base BC with A and D on opposite sides of line BC such that area

(Δ A B C)

= area

(Δ D B C)

. Show that BC bisects AD.

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If △ABC and △DBC are on the same base BC,AB=DC and AC=DB,then which of the following gives a CORRECT congruence relationship?

The correct option is D △ABC=△DCBIn triangle ΔABC and ΔDCB we haveAB=DC , AC=DB and BC=BCthen from SSS congruence ,ΔABC=ΔDCB

If $△ A B C$ and $△ D B C$ are on the same base BC,AB=DC and AC=DB,then which of the following gives a CORRECT congruence relationship?

The correct option is D $△ A B C = △ D C B$
In triangle $Δ A B C$ and $Δ D C B$ we have
$A B = D C$ , $A C = D B$ and $B C = B C$
then from $S S S$ congruence , $Δ A B C = Δ D C B$