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(𝑥 + 4) = 70
Prove: 𝑥 = −18
Statements
Reasons
1. −𝟓(𝒙 + 𝟒) = 𝟕𝟎
1. Given
2. −𝟓𝒙 − 𝟐𝟎 = 𝟕𝟎
2. Distribute (add to list)
3. −𝟓𝒙 = 𝟗𝟎
3. Addition
4. 𝒙 = −𝟏𝟖
4. Division
Given:
5𝑥+1
–8
2
Prove: 𝑥 = 3
=0
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 = 𝑡 ∙
Prove: 𝑢 =
2𝑑
𝑡
𝑢+𝑣
2
−𝑣
Given: < 𝐹𝐺𝐽 ≌< 𝐽𝐺𝐾, < 𝐽𝐺𝐾 ≌< 𝐾𝐺𝐻, 𝑚 < 𝐹𝐺𝐽 =
6𝑥 + 7, 𝑚 < 𝐾𝐺𝐻 = 8𝑥– 5
Prove: 𝑥 = 6
̅̅̅̅ ≌ ̅̅̅̅
Given: 𝐶𝐷
𝐸𝐹 , 𝐶𝐷 = 3𝑦 – 9, 𝐸𝐹 = 15
Given: −4(𝑥 – 3) + 5𝑥 = 24
Prove: 𝑦 = 8
Prove: 𝑥 = 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 – 𝑎)
𝑇
Prove: a = 220 - 0.75
Given:
8−3𝑥
4
= 32
Prove: 𝑥 = −40
1
1
Given: − 3 𝑛 = 12
Prove: 𝑛 = −36
1
Given: 5 𝑥 + 3 = 2𝑥 − 24
Given: −3𝑟 + 2 = 4
Prove: 𝑥 = 15
Prove: 𝑟 = − 6
7
Acceleration a in
𝑑 = 𝑣𝑡 +
1
𝑎𝑡 2 .
2
𝑓𝑡
,
𝑠𝑒𝑐 2
distance traveled d in feet, velocity v in
𝑓𝑡
,
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 𝑎 =
2𝑑−2𝑣𝑡
.
𝑡2
1
Given: 𝑑 = 𝑣𝑡 + 2 𝑎𝑡 2
Prove: 𝑎 =
2𝑑−2𝑣𝑡
𝑡2
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 ̅̅̅̅
𝐷𝐹 ≅ ̅̅̅̅
𝐸𝐺 , then x=10
temperature of the gas.
Given:________________________________________
Prove:________________________________________
Given:___________________________________________
Prove:___________________________________________
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅ , then x=4
If 𝐴𝐵
Given:_________________________________________
Prove:_________________________________________
If < 𝑌 ≅< 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:____________________________________________