Question

List the pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar triangles. Plz this is due today!!!! I tried 3 times already!!!! More in pic.

Answer 1

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Answer:

• angle pairs: correct
• EF/HI = EG/HJ = FG/IJ

Explanation:

As with the angle pairs, use the corresponding vertices to name corresponding segments.

As is done here, I find it convenient to list the vertices vertically in the order shown in the similarity statement.

• ∠E ≅ ∠H
• ∠F ≅ ∠I
• ∠G ≅ ∠J

This can make it easier to identify the corresponding vertices used for naming segments.

__

Moving on the the extended proportion, ...

The denominator HI uses the first two vertices, with E corresponding to H and F corresponding to I. The appropriate ratio is ...

EF/HI

The denominator HJ uses the 1st and 3rd vertices, with E (still) corresponding to H and J corresponding to G. The appropriate ratio is ...

EG/HJ

Similar thinking is used to identify the last ratio:

FG/IJ

Then the extended proportion is ...

EF/HI = EG/HJ = FG/IJ