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Geometry - Congruent Triangles










































triangle CDE is congruent to triangle FGH, angle G = (x+17), angle E = (19-x), angle H = (27-2x), line segment GH = 39-3x. Find line segment DE!

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Nov 08, 2011
Congruent Triangles
by: Staff

Question:

triangle CDE is congruent to triangle FGH, angle G = (x + 17), angle E = (19 - x), angle H = (27 - 2x), line segment GH = 39 - 3x. Find line segment DE!


Answer:

∠ H and ∠ E are corresponding angles

∠H = (27 - 2x)

∠E = (19 - x)


∠H = ∠E


(27 - 2x) = (19 - x)

27 - 2x = 19 - x


27 - 2x + 2x = 19 - x + 2x

27 + 0 = 19 - x + 2x

27 = 19 - x + 2x

27 = 19 + x

27 - 19 = 19 - 19 + x

8 = 19 - 19 + x

8 = 0 + x

8 = x

x = 8

∠H & ∠E = (27 - 2x)

= (27 - 2*8)

= (27 - 16)

= 11°


∠G = (x + 17)

= (8 + 17)

= 25°


∠F = 180 - ∠H - ∠G

= 180 - 11 - 25

= 144°


All three angles for △FGH are:

∠F = 144°

∠G = 25°

∠H = 11°


△FGH is an obtuse triangle (one angle is greater than 90 degrees)

△FGH is an scalene triangle (all three sides have different lengths)



The side (line segment) GH = 39 - 3x

= 39 - 3*8

= 39 - 24

= 15


The line segment DE in △CDE corresponds to the line segment GH in △FGH.


The final answer is: DE = 15



Open the link shown below to view △FGH drawn to scale :

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http://www.solving-math-problems.com/images/triangle-FGH-2011-11-07-01.png



Thanks for writing.

Staff
www.solving-math-problems.com



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