On a basic parallelogram, opposite sides are parallel, diagonals bisect each other and, consecutive angles are supplementary. However on a parallelogram diagonals aren't congruent.
So the answer is D
Answer:
y = -2x - 3
Step-by-step explanation:
The altitude will be a line perpendicular the the opposite side DE.
The slope of DE = (3 - -1) / (3 - -5)
= 4/8 = 1/2
So the slope of the altitude = -1 / 1/2 = -2
Thus the equation of the altitude through F (1, -5) can be found using the point-slope form y - y1 = m(x - x1):-
y - -5 = -2(x - 1)
y + 5 = -2x + 2
y = -2x + 2 - 5
y = -2x - 3 (answer)
Answer:
B
Step-by-step explanation:
The sum of all of them will result in 180. 15x-45=180. x=15. P=55, Q=70 and R=55. It's an isosceles triangle
Answer:
x = 16
Explanations:
Since △ACD ~ △ABE, it means that:
CD/AD = BE/AE..........(*)
CD = 3x + 8
AD = AE + ED
AD = (x - 1) + 27
AD = x + 26
BE = 20
AE = x - 1
Substituting CD, AD, BE, and AE into equation (*)
(3x+8)/(x+26) = 20/x-1
Cross multiply:
(3x+8)(x-1) = 20(x+26)
3x² - 3x + 8x - 8= 20x + 520
3x²- 15x - 528 = 0
Divide through by 3
x² - 5x - 176 = 0
Solving the quadratic equation above for the values of x
x² - 16x + 11x - 176 = 0
x(x - 16) + 11 (x - 16) = 0
(x - 16)(x + 11) = 0
If x - 16 = 0
x = 16
If x + 11 = 0
x = -11
x cannot be -11 because x = -11 will make side CD and AE to be negative, and the sides of a triangle cannot be negative.
Therefore, x = 16
All the steps arranged in the attachment!