Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent. given: c, f are rt. (angles) ; ab = de ; bc = ef

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The abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.

HL.

Step-by-step explanation:

The Figure is attached below

Given:

AB = DE ; BC = EF

∠C = ∠F = 90°

To Prove:

ΔACB ≅ ΔDFE

Proof:

Hypotenuse Leg Theorem:

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

The abbreviation is HL

In  ΔACB  and ΔDFE  

AB ≅ DE      ……….{Hypotenuse congruent Given}

BC  ≅ EF     ……….{Given}

∠C ≅ ∠F = 90°     …………..{Measure of each angle is 90° given}

ΔACB  ≅ ΔDFE   ….{Hypotenuse Leg ( HL ) Theorem}