Two triangles with the same corresponding side lengths will be congruent is known as the ____.
1 answer:
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Answer:
1. Given
2. Diagonals of a parallelogram bisect each other.
3. Vertical angles are equal.
4. Definition of parallelogram.
5. If lines parallel, then alternate interior angles are equal.
6. ASA
7. CPCTE
Step-by-step explanation:
Statement 1:
The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.
Statement 2:
BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence,
Statement 3:
Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.
Statement 4:
A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, is because of the definition of a parallelogram.
Statement 5:
Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.
Statement 6:
The triangles BET and DFT are now congruent because:
i.Angle-
ii. Side -
iii. Angle -
Therefore, by ASA postulate the two triangles are congruent.
Statement 7:
As the two triangles are congruent, then their corresponding parts are also equal.
So, by CPCTE,
Answer:
Step-by-step explanation:
Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB
=> MP là đường trung bình của tam giác DAB => MP//BD và MP=BD (1)
Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC
=> QN là đường trung bình của tam giác DBC => QN//BD và QN=BD (2)
Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN
và độ dài MP = độ dài QN = BD
=> vecto MP = vecto QN
Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN