Question 3 (multiple answer) Read and complete the following proof. The followin

ID: 3003681 • Letter: Q

Question

Question 3 (multiple answer)

Read and complete the following proof.

The following is a proof of the SSS Similarity Theorem.

Construct point G on DF¯ so that it is the midpoint of ___[1]____.

Construct point H on EF¯ so that it is the midpoint of EF¯.

Construct triangle ABC such that AB=GH, __________=GF, and BC=HF.

Due to the construction in Step 3 and the definition of congruent segments, AB¯?GH¯, AC¯?GF¯, and BC¯?HF¯.

Since all three pairs of corresponding sides are congruent, __________ by the SSS Congruence Postulate.

Since all congruent triangles are also similar, ?ABC??GHF.

Due to the constructions in steps 1 & 2, along with the definition of a midsegment, it can be stated that GH¯ is a midsegment of ?DFE.

According to the Midsegment Theorem, ___[2]____ ?DE¯.

Therefore, ?D??FGH and ?E??FHG since these are two pairs of corresponding angles on parallel lines cut by transversals.

Now that there are two pairs of congruent angles, it is possible to use the __________ to state that ?DEF??GHF.

Finally, the __________ Property of Similarity allows that since ?ABC??GHF and ?DEF??GHF, it can be concluded that ?ABC??GHF.

(Thus, given in the construction steps of 1 & 2, that ACDF=BCEF=ABDE, it is possible to conclude that ?ABC??GHF.)

Choose the appropriate names or words to fill in the blanks labeled [1] and [2] in the proof.

[2]: AB¯

[1]: DF¯

[2]: DE¯

[1]: GH¯

[1]: EF¯

[2]: GH¯