Question

Write a complete two-column proof for following information: Given: Segment AB = x + 16, Segment BC = 4x + 11 Segment AC = 77 Prove: AB = 26

Answer 1

Answer:

AB+BC=AC

x+16+4x+11=77

5x=77-27

5x=50

x=50/5

x=10

AB=x+16

AB=10+16

AB=26

x------HENCE PROVED--------x

Answer 2

When Segment AB = x + 16, Segment BC = 4x + 11 and Segment AC = 77, It is true that AB = 26.

Given:

Line segment,  AB = x + 16

Line Segment, BC = 4x + 11

Line Segment, AC = 77  

To find:

Prove that AB = 26

Solution:  

If we consider A, B and C are 3 collinear points and lie same line

⇒ AC = AB + BC

From given data

⇒ 77 = x + 16 + 4x + 11

⇒ 77 = 5x + 27

⇒ 5x = 50

⇒ x = 10

As we know AB = x + 16

⇒ AB = 10 + 16 = 26

⇒ AB = 26

Hence, It is proven that AB = 26

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