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Area of triangle = 1/2 . base . height
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The missing value is 12 in a system of equations with infinitely many solutions conditions.
It is given that in the system of equations there are two equations given:
It is required to find the missing value in the second equation.
<h3>What is a linear equation?</h3>It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
We have equations:
Let's suppose the missing value is 'Z'
We know that the two pairs of equations have infinitely many solutions if and if they have the same coefficients of variables and the same constant on both sides.
From equation (1)
(multiply both the sides by 3)
...(3)
By comparing the equation (2) and (3), we get
M = 12
Thus, the missing value is 12 in a system of equations with infinitely many solutions conditions.
Learn more about the linear equation.
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]
Learn more about parallelogram on:
#SPJ1
