Elena wants to prove that the measures of the 3 angles in a triangle always
sum to 180 degrees. She starts by using rigid motions to rotate triangle ABC
180° around 2 midpoints. Explain how Elena labeled her diagram and finish
her proof.
E
D
o
6
С
В
B
Answers
My best explanation to this question is:
Elena has summed the total of all three angles in the straight angle to get 180°; <DAB, <BAC , and <CAE. But this does not mean a total of three angles will ALWAYS equal 180°. If one angle is greater than the other two, then there is a possible chance the angle will not be 180°. If the angles are scalene, then there is a greater chance the angle may not be 180°.
This may be wrong, so you don’t have to come up with my response exactly, just modify it to what you need. Wish you luck.
The measures of the 3 angles in a triangle always sum to 180 degrees.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
We have to determine the prove that the measures of the 3 angles in a triangle always sum to 180 degrees.
We have been given that angles as
∠ DAB, ∠ BAC, and ∠ CAE.
Each 180-degree rotation takes line BC to a parallel line. So line DA is parallel to BC and line AE is also parallel to BC.
There is only one line parallel to BC that goes through point A, so lines DA and AE are the same lines.
Since line DE is parallel to line BC,
∵ alternate interior angles are congruent.
This represents that angle BAD also measures b" and angle CAE also measures c'. D
Since DE is a line, the 3 angle measures at point A would sum to 180 degrees.
So a + b + c = 180.
The fact that this explanation is dependent on the triangle we started with indicates that any triangle's sum of its three angles is always 180 degrees.
Therefore, the measures of the 3 angles in a triangle always sum to 180 degrees.
Learn more about the congruent triangles here:
brainly.com/question/4364353
#SPJ2
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