Congruent triangles

By convention, when we say two triangles are congruent, we list their vertices in the same order, so that corresponding parts are in the same places in the names: D corresponds to W, for example (because they are the first letter in each case), and DE corresponds to WX (because they are the first two letters).

List the pairs of corresponding vertices, and the pairs of corresponding sides. Then look at the four choices, and see which show only corresponding parts.
 
pka said:
The notation \(\displaystyle \Delta DEF\cong\Delta WXY\) tells us everything about the correspondences.
Therefore, only part c) can be correct. Can you explain why?
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In congruent triangles the corresponding parts (angles and sides) are congruent.
In a pair of similar triangles, corresponding sides are proportional and all three angles are congruent.

In a pair of similar triangles, the corresponding sides are proportional. Corresponding sides touch the same two angle pairs.
 
I would simply say that of the statements about angles, only E and X are corresponding angles (the middle letters), so the answer must be (A) or (C); then, looking at the statements about sides, DF corresponds to WY (first and last letters), not to XY, so only (C) is correct.
 
Dr.Peterson said:
I would simply say that of the statements about angles, only E and X are corresponding angles (the middle letters), so the answer must be (A) or (C); then, looking at the statements about sides, DF corresponds to WY (first and last letters), not to XY, so only (C) is correct.
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Can you tell me if my reasoning is enough?
11)
(C) shows corresponding parts to congruent triangles that are congruent.
In congruent triangles the corresponding parts (angles and sides) are congruent.
By convention, when we say two triangles are congruent, we list their vertices in the same order, so that corresponding parts are in the same places in the names: E corresponds to X, for example (because they are the first letter in each case), and EF corresponds to WY (because they are the first two letters).
 
That's basically what I said, just a little wordier, and without stating how you chose (C).

Your teacher is the one to tell you whether you have said enough; I am not the judge of that. Teachers can vary in how much they demand in written answers.
 
I'd list the 6 facts (3 involving angles, 3 involving sides) from the initial staement of congruent triangles. Then conclude that c is the only choice that's true.
 
Look at the choices for answers. They consist of one statement about angles, and one statement about sides - not necessarily correct.

Write the 3 correct statements about angles and the 3 correct statements for sides, using the triangle congruency statement given at the beginning of the question.
 
DEF = WXY
D corresponds to W
E corresponds to X
F corresponds to Y
DE corresponds to WX
EF corresponds to XY
 
They don't just correspond, they are congruent (ie equal in size).

"Angle D is congruent to Angle W" etc, better if you use the correct symbolism \(\displaystyle \angle{D} \cong \angle{W}\)

"Side DE is congruent to Side WX" or \(\displaystyle \overline{\rm DE}\cong\overline{\rm WX}\)

You've also missed the third side DF.
 
(C) shows corresponding parts to congruent triangles that are congruent.
In congruent triangles the corresponding parts (angles and sides) are congruent.
DEF = WXY
Angle D is congruent to Angle W
Angle E is congruent to Angle X
Angle F is congruent to Angle Y
Side DE is congruent to Side WX
Side EF is congruent to Side XY
Side DF is congruent to Side WY
By convention, when we say two triangles are congruent, we list their vertices in the same order, so that corresponding parts are in the same places in the names: E corresponds to X, for example (because they are the first letter in each case), and EF corresponds to WY (because they are the first two letters)
 
rachelmaddie said:
(C) shows corresponding parts to congruent triangles that are congruent.
In congruent triangles the corresponding parts (angles and sides) are congruent.
Triangle DEF is congruent to Triangle WXY (= means exactly the same triangle, is congruent to applies to two different triangles of same size)
Angle D is congruent to Angle W
Angle E is congruent to Angle X
Angle F is congruent to Angle Y
Side DE is congruent to Side WX
Side EF is congruent to Side XY
Side DF is congruent to Side WY
By convention, when we say two triangles are congruent, we list their vertices in the same order, so that corresponding parts are in the same places in the names: E corresponds to X, for example (because they are the first letter in each case), and EF corresponds to WY (because they are the first two letters)
Click to expand...
Good. Just try to use the correct language. (see red)
 
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