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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.

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 class=

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Answer:

See explanation

Step-by-step explanation:

1 step: [tex]\overline{GI}\cong \overline {JL}[/tex] - given

2 step: [tex]\overline{GI}\cong \overline{GH}+\overline{HI}[/tex] - Segments Addition Postulate

3 step: [tex]\overline{GH}+\overline{HI}\cong \overline {JL}[/tex] - Substitution Property

4 step: [tex]\overline {JL}\cong \overline {JK}+\overline {KL}[/tex] - Segments Addition Postulate

5 step: [tex]\overline{GH}+\overline{HI}\cong \overline {JK}+\overline {KL}[/tex] - Substitution Property

6 step: [tex]\overline{GH}\cong \overline {KL}[/tex] - given

7 step: [tex]\overline{GH}+\overline{HI}\cong \overline {JK}+\overline {GH}[/tex] - Substitution Property of Equality

8 step: [tex]\overline{HI}\cong \overline {JK}[/tex] - Subtraction Property of Equality

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

  • From the given image, we see two lines namely; GHI and JKL.

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.

Read more at; https://brainly.com/question/16733867

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