In the figure below, ΔGHF≅ΔEHD. Which statement is true by CPCTC?

a.∠EHF ≅ ∠GHF

b.∠DHE ≅ ∠DHG

c.∠HED ≅ ∠HFG

d.∠HDE ≅ ∠HFG

d.∠HDE ≅ ∠HFG

Step-by-step explanation:

we know that

CPCTC is an acronym for corresponding parts of congruent triangles are congruent

Remember that

If two triangles are congruent, then its corresponding angles and its corresponding sides are congruent

In this problem we have

ΔGHF≅ΔEHD

Corresponding angles are

∠HGF and ∠HED

∠GHF and ∠DHE

∠HFG and ∠HDE

so

∠G ≅ ∠E

∠H ≅ ∠H

∠F ≅ ∠D

Corresponding sides are

GH and EH

HF and HD

GF and ED

so

GH ≅ EH

HF ≅ HD

GF ≅ ED

therefore

The correct option is

d.∠HDE ≅ ∠HFG

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

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