Answer:
Step-by-step explanation:
Equal
<span>After the two cuts, 1 3/4 ft of the board is left.</span><span> </span>
Answer:
2/5
Step-by-step explanation:
Given Marcellus drank 1/4 gallon of the limeade and Marcy drank 1/8 gallon of the limeade
Given that only 5/8 portion of the pitcher contains limeade
Total amount drunk = amount drunk by Marcellus + amount drunk by Marcy
Total amount drunk = 
= 
The amount of Limeade remained = The amount initially - the amount drunk
The amount remained = 
= 
Fractional part = amount remained / amount initially = 
= 
Answer:
Yes since the triangles are congruent by ASA. See proofs and explanation below.
Step-by-step explanation:
The cardio and free weights will have the same amount of space because triangles ABE and BCE are congruent by ASA or Angle-Side-Angle. We know that angle AEB and angle DEC are congruent since they are vertical angles. This is the first angle is ASA. We also know that the two triangles must be congruent because line segment DE is congruent to line segment EB since E is the midpoint of DB. This is the side in ASA. Lastly, the other angle of ASA can be proven because AB and DC are parallel lines. SInce they are parallel they have special angle relationships when the transversal DB intersects them. Since angle ABE and angle EDC are alternate interior angles, they are congruent. This means the triangles must be congruent. When triangles are congruent, then each triangle is the same shape and size. This means their area is the same too. Therefore, cardio and free weights have the same amount of space.
To write a two columns proof, start with given information, add new information, and then conclude.
Statement Reason
1. AB ║CD Given
2. E midpoint of DB Given
3. DE ≅ EB Definition of Midpoint
4. ∠ABE≅∠EDC Alternate Interior Angles
5. ∠AEB ≅ ∠DEC Vertical Angle Theorem
6. ΔABE≅ΔCDE ASA
Use the angle relationships above and listed in number 4 to solve for the angle measures.
1. 62 and (4x+2) are alternating interior angles and they are equal
so
62 = 4x+2 now solve for x
2. vertical angles are straight across from each other
1 and 4
2 and 3
5 and 8
7 and 6
Alternate interior : alternate (or cross) the Transversal and are interior (inside) and are equal
4 and 5, 3 and 6
Corresponding are the angles in matching corners
1 and 5, 2 and 6, 3 and 7, 4 and 8
Alternate exterior : alternate (or cross) the Transversal and are exterior (outside)
2 and 7, 1 and 8,
