12. Yes, because the diagonals of a parallelogram bisect each other.
14. Yes, a parallelogram has opposite sides that are equal.
Hope this helps =)
Answer:
2
Step-by-step explanation:
8 + 6 - 12 = 2
Answer:
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 2. and then rotating it about the origin by 180 degrees
Step-by-step explanation:
Step 1: Dilation by a scale factor of 1/2.
A point (x, y) is sent to (1/2 x, 1/2 y).
A(2, 2) ---> (1, 1)
B(2, 10) ---> (1, 5)
C(8, 12) ---> (4, 6)
Step 2: Rotate about the origin 180 degrees
A point (x, y) is sent to (-x, -y).
(1, 6) ---> A'(-1, -1)
(1, 5) ---> B'(-1, -5)
(4, 6) ---> C'(-4, -6)
Applying the leg rule, and solving algebraically, the lengths are determined as:
JG = 9
HJ = 12
<h3>What is the Leg Rule?</h3>
The Leg rule states that when an altitude bisects the right angle of a right triangle and intersects the hypotenuse, then, hypotenuse/leg = leg/part.
Find length of JG using algebraic solutions and the leg rule:
Let JG = x
Hypotenuse = x + 16
Leg = 15
Part = x
Therefore:
(x + 16)/15 = 15/x (leg rule)
Cross multiply
x(x + 16) = (15)(15)
x² + 16x = 225
x² + 16x - 225 = 0
Factorize
(x + 25)(x − 9) = 0
x = -25 or x = 9
The length of JG (x) cannot be negative, therefore, the length of JG = 9.
Find length of JG using algebraic solutions:
Let HJ = y
Based on the altitude theorem, we would have:
y = √(16 × JG)
Substitute
y = √(16 × 9)
y = √(144)
y = 12
Therefore, the length of HJ is: 12.
Learn more about the leg rule on:
brainly.com/question/25016594
