Segment gi is congruent to segment jl and segment gh is congruent to segment kl. i have to prove segment hi is congruent to segment jk. it has to be done in eight steps with reasons.

The 8 steps showing the 8 statements and reasons to prove that HI ≅ JK has been explained below.

We want to prove that HI ≅ JK

We are given the statement; GI ≅ JL

This means line GI is congruent and thus equal to Line JL.

Statement 2; GI = GH + HI

The reason is we used segment addition postulate since point H is a point on line GI.

Statement 3; GH + HI = JL

Reason is because of use of substitution property since GI ≅ JL.

Statement 4; JL = JK + KL

The reason is we used segment addition postulate since point K is a point on line JL.

Statement 5; GH + HI = JK + KL

Reason is because of use of substitution property since GH + HI = JL.

Statement 6; GH ≅ KL

Reason is because we are given that in the question

Statement 7; GH + HI ≅ JK + GH

Reason is use of substitution property since GH ≅ KL

Statement 8; HI ≅ JK

Reason is subtraction property of equality where GH was subtracted from both sides.

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See explanation

Step-by-step explanation:

1 step: - given

2 step: - Segments Addition Postulate

3 step: - Substitution Property

4 step: - Segments Addition Postulate

5 step: - Substitution Property

6 step: - given

7 step: - Substitution Property of Equality

8 step: - Subtraction Property of Equality

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Step-by-step explanation: