Answer:
A
Step-by-step explanation:
Reflecting it across the lines will bring the triangle on to the other triangles. This will show that when the triangle goes under a transformation such as reflection, the angles will stay the same.
Angle 1 and angle 5 are equal so you can set the equations equal to each other. 60 - 2x = 70 - 4x
60 + 2x = 70
2x = 10
x= 5
Answer:
The first term is 13/3 and the common difference is d = 1/12
The formula is a(n) = 13/3 + (1/12)(n - 1)
Step-by-step explanation:
The general equation for an arithmetic progression is:
a(n) = a(1) + d(n - 1), where d is the common difference/
Case 1: n = 7: 29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)
Case 2: n = 15: 11/2 = a(1) + d(15 - 1) = a(1) + d(14)
Then our system of linear equations is:
a(1) + 6d = 29/6
a(1) + 14d = 11/2
Let's solve this by elimination by addition and subtraction. Subtract the first equation from the second. We get:
Substituting 1/12 for d in the first equation, we get:
a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)
Then a(1) = 66/12 - 14/12 = 52/12 = 13/3
The first term is 13/3 and the common difference is d = 1/12
The arithmetic sequence formula for this problem is thus:
a(n) = 13/3 + (1/12)(n - 1) 8
-x + 7 = x - 5
add x to both sides of the equation
7 = 2x - 5
add 5 to both sides of the equation
12 = 2x
divide 2 from both sides of the equation
6 = x
Answer:
Given: In triangle ABC and triangle DBE where DE is parallel to AC.
In ΔABC and ΔDBE
[Given]
As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.
Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]
Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.
then;
and
Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.
by Reflexive property of equality:
By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar
therefore, by AAA similarity postulates theorem
Similar triangles are triangles with equal corresponding angles and proportionate side.
then, we have;
[By definition of similar triangles]
therefore, the missing statement and the reasons are
Statement Reason
3. Corresponding angles theorem
and
5. AAA similarity postulates
6. BD over BA Definition of similar triangle
