Proofs Test Review

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Name_________________________________________
Period_________
Date_____________________
CP Geometry Algebraic Proofs
Write a two-column proof for each of the following. Make sure to create a T-chart and label “Statements” and
“Reasons” and then number each line that you put in your proof.
Given: −5(π‘₯ + 4) = 70
Prove: π‘₯ = −18
If the distance d moved by and object with initial
velocity u and final velocity v in time t is given, prove
the following:
Given: 𝑑 = 𝑑 βˆ™
Prove: 𝑒 =
2𝑑
𝑑
𝑒+𝑣
2
−𝑣
Given: < 𝐹𝐺𝐽 β‰Œ< 𝐽𝐺𝐾, < 𝐽𝐺𝐾 β‰Œ< 𝐾𝐺𝐻, π‘š < 𝐹𝐺𝐽 =
6π‘₯ + 7, π‘š < 𝐾𝐺𝐻 = 8π‘₯– 5
Given: < 5 ≅< 6
Prove: < 4 and < 6 are supplementary
Prove: π‘₯ = 6
Μ…Μ…Μ…Μ… β‰Œ Μ…Μ…Μ…Μ…
Given: 𝐢𝐷
𝐸𝐹 , 𝐢𝐷 = 3𝑦 – 9, 𝐸𝐹 = 15
Given: −4(π‘₯ – 3) + 5π‘₯ = 24
Prove: 𝑦 = 8
Prove: π‘₯ = 12
Given:
𝑦+2
3
=3
Prove: 𝑦 = 7
Mae measures her heart rate whenever she exercises
and tries to make sure that she is staying in her target
heart rate zone. The American Heart Association
suggests a target heart rate of T = 0.75(220 – a),
where T is a person’s target heart rate and a is his or
her age. Prove that given the formula for heart rate,
you can calculate his or her age using the formula a =
𝑇
220 0.75
Given: 𝑇 = 0.75(220 – π‘Ž)
𝑇
Prove: a = 220 - 0.75
Given:
8−3π‘₯
4
= 32
Prove: π‘₯ = −40
1
1
Given: − 3 𝑛 = 12
Prove: 𝑛 = −36
1
Given: 5 π‘₯ + 3 = 2π‘₯ − 24
Given: −3π‘Ÿ + 2 = 4
Prove: π‘₯ = 15
Prove: π‘Ÿ = − 6
7
Acceleration a in
𝑑 = 𝑣𝑑 +
1
π‘Žπ‘‘ 2 .
2
𝑓𝑑
,
𝑠𝑒𝑐 2
distance traveled d in feet, velocity v in
𝑓𝑑
,
𝑠𝑒𝑐
and time t in seconds are related in the formula
Prove that if the values for distance, velocity and time are known, then the acceleration of an object
can be calculated using the formula π‘Ž =
2𝑑−2𝑣𝑑
.
𝑑2
1
Given: 𝑑 = 𝑣𝑑 + 2 π‘Žπ‘‘ 2
Prove: π‘Ž =
2𝑑−2𝑣𝑑
𝑑2
Write the given statement(s) and the prove statement on the lines provided. Then write a two-column proof.
The Ideal Gas Law is given by the formula 𝑃𝑉 = 𝑛𝑅𝑇,
where P=pressure in atmospheres, V=volume in
liters, n=amount of gas in moles, R is a constant
value, and T=temperature in degrees Kelvin. Prove
that if the pressure, volume and amount of gas are
𝑃𝑉
known, then the formula 𝑇 = 𝑛𝑅 gives the
If Μ…Μ…Μ…Μ…
𝐷𝐹 ≅ Μ…Μ…Μ…Μ…
𝐸𝐺 , then x=10
temperature of the gas.
Given:________________________________________
Prove:________________________________________
Given:___________________________________________
Prove:___________________________________________
Μ…Μ…Μ…Μ… ≅ 𝐴𝐢
Μ…Μ…Μ…Μ… , then x=4
If 𝐴𝐡
Given:_________________________________________
Prove:_________________________________________
If < π‘Œ ≅< 𝑍, then x=100
If < 𝑀𝑃𝑁 ≅< 𝑄𝑃𝑁, then x=16
Given:____________________________________________
Prove:____________________________________________
The voltage V of a circuit can be calculated using the
𝑃
formula, 𝑉 = 𝐼 , where P is the power and I is the
current of the circuit. Write a proof to show that
when the current is constant, the voltage is doubled
when the power is doubled.
Given:____________________________________________
Given:______________________________________________
Prove:______________________________________________
Prove:____________________________________________
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