Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 7 x 5 = \( \frac{35}{2} \) = 17\(\frac{1}{2}\)

You need to find the value of c so solve the first equation in terms of z:

4c + z = 6
z = 6 - 4c

then substitute the result (6 - 4c) into the second equation:

-8c - 5(6 - 4c) = 8
-8c + (-5 x 6) + (-5 x -4c) = 8
-8c - 30 + 20c = 8
-8c + 20c = 8 + 30
12c = 38
c = \( \frac{38}{12} \)
c = 3\(\frac{1}{6}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

5a - 7a = -2a

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).