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Math  /  Geometry

QuestionWhich postulate or theorem proves that △CFE\triangle C F E and △DFE\triangle D F E are congruent? SAS Congruence Postulate AAS Congruence Theorem HL Congruence Theorem SSS Congruence Postulate

Studdy Solution

STEP 1

1. △CFE \triangle CFE and △DFE \triangle DFE are right triangles.
2. ∠CEF \angle CEF and ∠DEF \angle DEF are right angles.
3. CF=DF CF = DF , indicating that the hypotenuses of the triangles are equal.
4. FE FE is a common side to both triangles.

STEP 2

1. Identify the type of triangles involved.
2. Determine the known sides and angles.
3. Choose the appropriate postulate or theorem for proving congruence.

STEP 3

Identify the type of triangles involved:
Both △CFE \triangle CFE and △DFE \triangle DFE are right triangles because they have a right angle at E E .

STEP 4

Determine the known sides and angles:
1. ∠CEF=∠DEF=90∘ \angle CEF = \angle DEF = 90^\circ (right angles).
2. CF=DF CF = DF (hypotenuses are equal).
3. FE FE is a common side to both triangles.

STEP 5

Choose the appropriate postulate or theorem for proving congruence:
Since both triangles are right triangles, and we know the hypotenuse and one leg (FE FE ) are equal, we use the Hypotenuse-Leg (HL) Congruence Theorem.
The postulate or theorem that proves △CFE \triangle CFE and △DFE \triangle DFE are congruent is:
HL Congruence Theorem \boxed{\text{HL Congruence Theorem}}

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