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Statement

1. Parallelogram ABCD with diagonals AC and BD
2.BC|| AD
3.CBD= ADB and BCA = DAC
4.BC = AB
5. AED = CEB
6. DE=BE and AE= CE

Statement 1. Parallelogram ABCD with diagonals AC and BD 2.BC|| AD 3.CBD= ADB and-example-1
User Paul John
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1 Answer

3 votes

Answer:

1. Parallelogram ABCD with diagonals AC and BD

DEFINITION OF PARALLELOGRAM.

2.B C || AD DEFINITION OF PARALLELOGRAM.

3.CBD= ADB and BCA = DAC (ASA) property

4.BC = AB CPCTC ( Corresponding parts of a congruent triangle)

5. AED = CEB (ASA) property

6. DE=BE and AE= CE : DEFINITION OF PARALLELOGRAM.

Explanation:

Here, given: ABCD is a parallelogram.

AC and BD are diagonals.

Now, consider the given statements one by one:

1. Parallelogram ABCD with diagonals AC and BD.

This information is already by DEFINITION OF PARALLELOGRAM.

2.BC|| AD

Definition of a parallelogram as Opposite sides in the parallelogram are EQUAL and PARALLEL.

3. ΔCBD = ΔADB and ΔBCA = ΔDAC

Now, here: as the opposites are parallel.

So, they form a pair of ALTERNATE angles.

Also, CB is a common segment in both triangle. and AC is common segment in second pair of triangles. ( REFLEXIVE Property of congruence)

Hence, ΔCBD = ΔADB and ΔBCA = ΔDAC by ANGLE SIDE SINGLE (ASA) property

4.BC = AB

CPCTC ( Corresponding parts of a congruent triangle)

5. ΔAED = ΔCEB

Now, here: as the opposites are parallel.

So, they form a pair of ALTERNATE angles.

Also, opposites are equal. ⇒ AD = BC

⇒ ΔAED = ΔCEB by ANGLE SIDE SINGLE (ASA) property

6. DE = BE and AE = CE

As, given AC and BD are diagonals.

Also, in a parallelogram, DIAGONALS BISECT EACH OTHER.

⇒DE = BE and AE = CE by DEFINITION OF PARALLELOGRAM.

User Zahiro Mor
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7.5k points