Given: ΔDFE is isosceles with base FE; FB ≅ EC.
Prove: ΔDFB ≅ ΔDEC
Triangle D F E is shown. 2 lines drawn down from point D to points C and B on the base of the triangle to form 3 triangles.
Complete the missing parts of the paragraph proof.
We know that 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.