Given: ΔDFE is isosceles with base FE; FB ≅ EC. Prove: ΔDFB ≅ ΔDEC Complete the missing parts of the paragraph proof. We know th
at triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent to segment by the definition of isosceles triangle. Since these segments are congruent, the base angles, angles , are congruent by the isosceles triangle theorem. Therefore, triangles are congruent by SAS
2 answers:
Answer:
Step-by-step explanation:
Given: ΔDFE is isosceles with base FE; FB ≅ EC.
To prove: ΔDFB ≅ ΔDEC
Proof: It is given that ΔDFE is isosceles with base FE; FB ≅ EC, thus
From ΔDFB and ΔDEC, we have
FB≅EC (Given)
DF≅DE (Definition of isosceles triangle)
∠DFE≅∠DEF⇒∠DFB≅DEC (because DF≅DE, therefore base angles are equal)
Thus, by SAS rule,
ΔDFB ≅ ΔDEC
Statements Reasons
1. FB≅EC (Given)
2. DF≅DE (Definition of isosceles triangle)
3.∠DFE≅∠DEF
⇒∠DFB≅DEC (because DF≅DE, therefore base angles are equal)
4. ΔDFB ≅ ΔDEC SAS rule
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