The complete proof for the given parallelogram is given in the image attached below.
<h3>What is a Parallelogram?</h3>
A parallelogram is a quadrilateral whose opposite sides are parallel and also congruent to each other.
The complete proof would be as shown below:
1. ABCD is a parallelogram [given]
2. AB║CD [Definition of parallelogram]
3. ∠1 ≅ ∠2, ∠3 ≅ ∠4 [alternate interior angles theorem]
4. AB ≅ CD [Definition of parallelogram]
5. ΔABE ≅ ΔCDE [ASA]
6. AE ≅ CE, BE ≅ DE [CPCTC]
7. AC and BD bisects each other at E [definition of segment bisector]
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Answer:
z = 8
Step-by-step explanation:
3/4 (z+4)=9
3/4z + 3 = 9
3/4z = 6
z = 8
Answer: x=−3
Step-by-step explanation: Let's solve your equation step-by-step.
2
3
(3x+9)=−2(2x+6)
Step 1: Simplify both sides of the equation.
2
3
(3x+9)=−2(2x+6)
(
2
3
)(3x)+(
2
3
)(9)=(−2)(2x)+(−2)(6)(Distribute)
2x+6=−4x+−12
2x+6=−4x−12
Step 2: Add 4x to both sides.
2x+6+4x=−4x−12+4x
6x+6=−12
Step 3: Subtract 6 from both sides.
6x+6−6=−12−6
6x=−18
Step 4: Divide both sides by 6.
6x
6
=
−18
6
x=−3
Answer:
x = 10 , 45 degrees.
Step-by-step explanation:
This seems a tricky one .
I guess we can use sin A + sin B = 2 sin (A+B)/2 cos (A - B) / 2
so sin 5x + sin x = 2 sin 3x cos 2x so our equation becomes
2 sin 3x cos 2x - cos 2x = 0
cos 2x ( 2 sin 3x - 1) = 0
so 2 sin 3x = 1
sin 3x = 1/2
giving 3x = 30 degrees and x = 10 degrees
or cos 2x = 0
so 2x = 90
giving x = 45 degrees.
Answer y=x,3x+3y+0
Step-by-step explanation:
