Look at the parallelogram ABCD shown below:

A parallelogram ABCD is drawn with BD as the diagonal. Angle ABD labeled angle 1. Angle CDB labeled angle 2. Angle CBD labeled angle 3. Angle ADB labeled angle 4.

The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:

Statement Reasons
1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram
2 angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the alternate interior angles are congruent
3 BD = BD Reflexive Property
4 triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent by _______________
5 AB = DC,
AD = BC Corresponding parts of congruent triangles are congruent

Which choice completes the missing information for reason 4 in the chart?
AAS postulate
ASA postulate
HL Postulate
SAS postulate

Question

02-10-2018
Mathematics

contestada

Look at the parallelogram ABCD shown below:

A parallelogram ABCD is drawn with BD as the diagonal. Angle ABD labeled angle 1. Angle CDB labeled angle 2. Angle CBD labeled angle 3. Angle ADB labeled angle 4.

The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:

Statement Reasons
1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram
2 angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the alternate interior angles are congruent
3 BD = BD Reflexive Property
4 triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent by _______________
5 AB = DC,
AD = BC Corresponding parts of congruent triangles are congruent

Which choice completes the missing information for reason 4 in the chart?
AAS postulate
ASA postulate
HL Postulate
SAS postulate

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Аноним Аноним · Answer 1 · 2018-10-12T12:21:47+02:00

Answer:

Given : A parallelogram ABC D in which BD is the Diagonal.

∠ABD =1, ∠ CDB =2, ∠CBD =3, ∠ ADB =4

To prove: Opposite sides of parallelogram are congruent.

Proof : AB is parallel to DC and AD is parallel to BC Definition of parallelogram

2 angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the alternate interior angles are congruent

3 BD = BD Reflexive Property

4 triangles ADB and CBD are congruent [If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent by[ ASA]

5 AB = DC,

AD = BC Corresponding parts of congruent triangles are congruent

Out of four options given

2. ASA postulate is the correct answer

A- angle, S-side,A-angle

Snazzysnoopy Snazzysnoopy · Answer 2 · 2018-12-26T17:54:06+01:00

Snazzysnoopy Snazzysnoopy

26-12-2018

Answer:

ASA postulate is the answer

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