Answer:
D. AC ≅ XZ
Step-by-step explanation:
To prove that two triangles are congruent by the Angle-Side-Angle theorem, both triangles must have two corresponding angles that are congruent to each other in each triangle, and also a corresponding included side in each triangle that are congruent.
Thus, we are given that,
<X ≅ <A and <Z ≅ <C, therefore, what is needed is a corresponding included angle in each triangle that are congruent to each other, which are,
AC and XZ
Therefore, what is needed is:
AC ≅ XZ
Since the triangles are similar, all sides are proportional by the same scale factor.
The relationship between the bases 32 and 8 is 4 (32/8 = 4). This means that the smaller triangle need to be multiplied by a scale factor 4 to result in the bigger triangle.
This means that 4x + 12 is 4 times greater than 15.
The equation to solve for x can be written as:
4x + 12 = 4*15
Now just solve for x as u normally would
4x + 12 = 60
(Subtract twelve from both sides)
4x = 48
(Divide both sides by 4 to isolate x)
x = 12
I hope this somewhat helped :)
Was my explanation clear enough?
Does x equal 4 ?if it does then a) -100
b) 25
Using theorem about secant segments we can write,
AB*AH=AG*AC
AC=4,
CG=6
AG=AC+CG=4+6=10
AH=3
AB= AH+HB=AH+x=3+x
(3+x)*3=10*4
9+3x=40
3x=40-9
3x=31
x=31/3≈10.3
HB≈10.3
EG=HB/2 (as radius and diameter)
EG=10.3/2≈5.2
