4) If C, P, and T are the midpoints of the sides
1 answer:
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Short Answers:
Answer for part A: Given
Answer for part B: Angle A = Angle D (not sure why this isn't in word bank?)
Answer for part C: ASA
Answer for part D: BC = EF
Answer for part E: CPCTC
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Explanations:
Part A:
AB = DE is given at the very top of the problem. So we simply say "given". We always repeat what we are given at the very start of the proof. You can see this for lines 1 through 3, which are repeating the three givens.
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Part B:
The three givens are:
AB = DE
angle A = angle D
angle B = angle E
the first and last of this trio is used (for statements 1 and 3 respectively). So the only thing left is "angle A = angle D"
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Part C:
We're using ASA (angle side angle) because we're given two pairs of congruent angles. The side for each triangle is between the two angles. See the attached diagram for more info.
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Part D:
For any proof, you will ALWAYS have the last statement be the thing you want to prove. In this case, we want to prove BC = EF.
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Part E:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
If the two whole triangles are congruent, then the smaller corresponding parts that make up the triangles must be congruent as well.
Answer for part A: Given
Answer for part B: Angle A = Angle D (not sure why this isn't in word bank?)
Answer for part C: ASA
Answer for part D: BC = EF
Answer for part E: CPCTC
-------------------------------------------------------------
Explanations:
Part A:
AB = DE is given at the very top of the problem. So we simply say "given". We always repeat what we are given at the very start of the proof. You can see this for lines 1 through 3, which are repeating the three givens.
---------------------
Part B:
The three givens are:
AB = DE
angle A = angle D
angle B = angle E
the first and last of this trio is used (for statements 1 and 3 respectively). So the only thing left is "angle A = angle D"
---------------------
Part C:
We're using ASA (angle side angle) because we're given two pairs of congruent angles. The side for each triangle is between the two angles. See the attached diagram for more info.
---------------------
Part D:
For any proof, you will ALWAYS have the last statement be the thing you want to prove. In this case, we want to prove BC = EF.
---------------------
Part E:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
If the two whole triangles are congruent, then the smaller corresponding parts that make up the triangles must be congruent as well.