Question

In each pair of triangles in the following figures, parts indicated by identical marks are congruent. A test of congruence of triangles is given below each figure. State the additional information which is necessary to show that the triangles are congruent by the given test. With this additional information, state the one to one correspondence in which the triangles will be congruent.

Answer 1

hey mate here's ur ans ↓↓

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⑴ In LMN and ∆ FDE

In order to be congruent ,

The sides LN and FE the hypotenuse must be equal , so that the triangles are congruent by RHS condition.

⑵In ∆ ABC and ∆ ADC,

In order to be congruent by ASA rule,

The following sides or angles must be equal,

∠CAD = ∠ACB
AC = AC
∠ ACD = ACB

∴∆ ABC ≈ ∆ ADC ( A.S.A)

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hope it helps u☺☺✌

Answer 2

Solution :

1 ) From figure ( i ),

In ∆LMN and ∆EDF

<M = <D = 90° [ Right angle ]--( 1 )

LN = FE ( Hypotenuse ] ---( 2 )

MN = DF ( Side ) ---( 3 )

To proof ∆LMN is congruent to ∆EDF

we need the information ( 2 ).

2 ) From figure ( ii ),

In ∆ACB and ∆CAD

<BAD = <ECB (Angle)--( 1 )

AD = EC ( Side ) ---( 2 )

<BDA = <CEB (Angle)--( 3 )

To prove ∆ACB is congruent to ∆CAD

required information is

( 3 ).

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