proofs practice
cut + paste activity
directions: cut out the answer options from the bottom of the page and paste them in for the correct reason. (tip:
use a pencil to write in each reason in the place you think it goes until youre ok sure you want to paste them
given: $ \angle a $ and $ \angle b $ are complementary
$ \angle c $ and $ \angle d $ are complementary
prove: $ \angle a \cong \angle d $
1. $ \angle a $ and $ \angle b $ are complementary
2. $ \angle c $ and $ \angle d $ are complementary
3. $ m \angle a + m \angle b = 90 ^ { \circ } $
4. $ m \angle c + m \angle d = 90 ^ { \circ } $
5. $ \angle b \cong \angle c $
6. $ m \angle b = m \angle c $
7. $ m \angle a + m \angle b = m \angle c + m \angle d $
8. $ m \angle a + m \angle c = m \angle c + m \angle d $
9. $ m \angle a = m \angle d $
10. $ \angle a \cong \angle d $
definition of
congruence
transitive
property
given
definition of
complementary
vertical angle
theorem
substitution
property
definition of
congruence
definition of
complementary
subtraction
property
given

Question

Accepted Answer

# Explanation:
## Step1: Statement 1 Reason
Given.
## Step2: Statement 2 Reason
Given.
## Step3: Statement 3 Reason
Definition of complementary (if two angles are complementary, the sum of their measures is $90^{\circ}$).
## Step4: Statement 4 Reason
Definition of complementary (if two angles are complementary, the sum of their measures is $90^{\circ}$).
## Step5: Statement 5 Reason
Vertical Angle Theorem (vertical angles are congruent).
## Step6: Statement 6 Reason
Definition of congruence (if two angles are congruent, their measures are equal).
## Step7: Statement 7 Reason
Substitution property (since $m\angle A + m\angle B=90^{\circ}$ and $m\angle C + m\angle D = 90^{\circ}$, we substitute $90^{\circ}$ with each other).
## Step8: Statement 8 Reason
Substitution property (substitute $m\angle B$ with $m\angle C$ from statement 6).
## Step9: Statement 9 Reason
Subtraction property (subtract $m\angle C$ from both sides of $m\angle A + m\angle C=m\angle C + m\angle D$).
## Step10: Statement 10 Reason
Definition of congruence (if the measures of two angles are equal,  the angles are congruent).

# Answer:
1. Given
2. Given
3. Definition of complementary
4. Definition of complementary
5. Vertical Angle Theorem
6. Definition of congruence
7. Substitution property
8. Substitution property
9. Subtraction property
10. Definition of congruence

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Question

Explanation:

Step1: Statement 1 Reason

Step2: Statement 2 Reason

Step3: Statement 3 Reason

Step4: Statement 4 Reason

Step5: Statement 5 Reason

Step6: Statement 6 Reason

Step7: Statement 7 Reason

Step8: Statement 8 Reason

Step9: Statement 9 Reason

Step10: Statement 10 Reason

Answer: