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Given:
ABC is an isosceles triangle in which AC =BC.
D and E are points on BC and AC such that CE=CD.
To prove:
Triangle ACD and BCE are congruent.
Solution:
In triangle ACD and BCE,
(Given)
(Common angle)
(Given)
In triangles ACD and BCE two corresponding sides and one included angle are congruent. So, the triangles are congruent by SAS congruence postulate.
(SAS congruence postulate)
Hence proved.
Answer x=5, y= 3.5
Find y by plugging the x value into the 2nd equation
4(2y-2) -9=11
8y - 8 - 9 =11 combine like terms
8y = 28 divide both sides by 8
y = 3.5
Now find x
Plug your y value into first equation
X = 2(3.5) -2
X= 7-2
X=5
You can check your work by putting your x or y values into the equations
For the first equation
5=2(3.5) -2
5=5
For the second equation
4(5) -9 = 11
20 - 9 = 11
11 =11
Find y by plugging the x value into the 2nd equation
4(2y-2) -9=11
8y - 8 - 9 =11 combine like terms
8y = 28 divide both sides by 8
y = 3.5
Now find x
Plug your y value into first equation
X = 2(3.5) -2
X= 7-2
X=5
You can check your work by putting your x or y values into the equations
For the first equation
5=2(3.5) -2
5=5
For the second equation
4(5) -9 = 11
20 - 9 = 11
11 =11