The algebra of triangles 1-5
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See below.

Step-by-step explanation:

1.

Corresponding angles of similar triangles are congruent.

m<C = m<C'

4x - 30 = x + 15

3x = 45

x = 15

m<C = 4x - 30 = 4(15) - 30 = 60 - 30 = 30

m<C' = m<C = 30

m<A = 2x + 35 = 2(15) + 35 = 30 + 35 = 65

2.

Method: SAS

BC = AD

6a + 20 = a + 60

5a = 40

a = 8

AB = 5a - 12 = 5(8) - 12 = 40 - 12 = 28

BC = 6a + 20 = 6(8) + 20 = 48 + 20 = 68

CD = AB = 28

AD = a + 60 = 8 + 60 = 68

3.

Method: SAS

2x + 3y = 34

4x - y = 40

Multiply the second equation by 3:

12x - 3y = 120

Add this new equation to the first original equation to eliminate y.

14x = 154

x = 11

Substitute 11 for x in the second original equation and solve for y.

4x - y = 40

4(11) - y = 40

44 - y = 40

-y = -4

y = 4

4.

Method: ASA

2d + 10 = 45 - 3d

5d = 35

d = 7

AC = 45 - 3d = 45 - 3(7) = 45 - 21 = 24

EC = 2d + 10 = 2(7) + 10 = 14 + 10 = 24

DE = d + 8 = 7 + 8 = 15

5.

2x - 59 = x + 31

x = 90

DO = x + 31 = 90 + 31 = 121

OG = 2x - 59 = 2(90) - 59 = 180 - 59 = 121

DG = x - 7 = 90 - 7 = 83

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: