Answer:
<u>Segment</u><u> </u><u>Addition</u><u> </u><u>Postulate</u>
<u>BC</u> + <u>AB</u> = <u>CA</u> [BOTH answers]
<u>Application</u><u> </u><u>with</u><u> </u><u>Midpoint</u>
<u>BC</u> = <u>BA</u>
1a) 9 = <em>x</em>
1b) 34 = FA
1c) 3 = AT
2a) 11 = <em>x</em>
2b) 37 = BO
2c) 37 = OX
2d) 74 = BX
Step-by-step explanation:
The Segment Addition Postulate is basically saying that if
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point <em>B</em><em> </em>is in between <em>AC</em><em> </em>[NOT<em> </em>the <em>midpoint</em><em> </em>(or halfway)],<em> </em>then both segments [AB and BC] would make up the whole thing [CA, or vice versa]. They are just explaining it in two unique ways you can word it.
The Midpoint Application tells you that if point <em>B</em><em> </em>is a
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<em>midpoint</em><em>,</em><em> </em>meaning <em>B</em> is halfway in between <em>AC</em><em>,</em><em> </em>then both segments [AB and BC] are congruent to each other.
1a) 37 = [2<em>x</em> - 15] + [3<em>x</em> + 7]
37 = 5<em>x</em> - 8
+ 8 + 8
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45 = 5<em>x</em>
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5 5
9 = <em>x</em>
1b) Solving for FA
1c) Solving for AT
This obviously had to be the answer because 3 + 34 = 37.
2a) 2<em>x</em> +15 = 4<em>x</em> - 7
- 4<em>x</em> - 4<em>x</em>
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-2<em>x</em> + 15 = -7
- 15 -15
_____________
-2<em>x</em> = -22
<em>x</em><em> </em>= 11
2b) Solving for BO
2c) Solving for OX
2d) Solving for BX
I am joyous to assist you anytime.