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anonymous
 one year ago
If Triangle ABC ~ triangle DEC solve for x. Picture not drawn to scale.
a. x=2
b. x=3
c. x=3
d. x=13
anonymous
 one year ago
If Triangle ABC ~ triangle DEC solve for x. Picture not drawn to scale. a. x=2 b. x=3 c. x=3 d. x=13

This Question is Closed

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1First, you need to find which sides are corresponding sides. dw:1437336453516:dw Complete the sentences below: Side 1 corresponds to side Side 2 corresponds to side Side 3 corresponds to side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0side 1 corresponds to side 4 side 2 corresponds to side 5 side 3 corresponds to side 6 i think

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1This is a little tricky, that why I asked. 1 corresponds to 4. That is correct. now let's look at the other sides. Since sides 1 and 4 are parallel, we can conclude some pairs of angles are congruent by interior angles of parallel lines cut by a tranversal.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437337115089:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You understand how the pairs of corresponding angles are congruent?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. I'll backtrack.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's start with 2 parallel lines. Lines m and n are given as parallel. dw:1437337278594:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we draw a transversal. Line t is a transversal to lines m and n. Angles 1 and 2 are alternate interior angles. When parallel lines are cut by a transversal, alternate interior angles are parallel. That means angles 1 and 2 are congruent. dw:1437337364835:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we draw another tranversal, line u. We find 2 alternate interior angles, labeled 3 and 4, and we know they must be congruent. dw:1437337588277:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Notice, we have the same drawing as your problem. The other two angles of the triangles are also congruent because they are vertical angles. dw:1437337682486:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1As you can see, our two triangles are similar. There are 3 pairs of congruent corresponding angles.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now let's get back to our problem. We need to figure out which pairs of sides are corresponding.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437337781397:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The three angles of the two triangles are marked with 1 line, 2 lines or 3 lines. Each side included by corresponding angles is corresponding. Look at side 1 on the left. Its angles have 1 mark and 2 marks. Then look at side 4. Its angles also have 1 mark and 2 marks. Side 1 and side 4 are corresponding. dw:1437337945253:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Sides 2 and 6 have 2 marks and 3 marks on the angles at their ends, so sides 2 and 6 are corresponding sides. See figure below. dw:1437337994043:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Finally, we do the same for sides 3 and 5. Side 3 and 5 are corresponding. dw:1437338122927:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok i understand that now

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now that we know which sides are corresponding sides, we can write a proportion of side lengths. \(\dfrac{AC}{DC} = \dfrac{BC}{EC} \) \(\dfrac{6}{8 + x} = \dfrac{11x}{19  2x} \) Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We solve the equation by cross multiplying. \(6(19  2x) = (8 + x)(11  x) \) \(114  12x = 88  8x + 11x  x^2\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(x^2  15 x + 26 = 0\) \((x  13)(x  2) = 0\) \(x = 13\) or \(x = 2\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now let's look at all sides and plug in 2 and 13 for x and calculate all lengths: Side x = 2 x = 13 6 6 6 8 + x 10 21 11  x 9 2 19  2x 15 7 Notice that when we use x = 13, some sides end up with a negative length. Since the length of the side of a triangle must be positive, x = 13 is eliminated, and the solution is x = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i understand it now, thank you for all the help!
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