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Quadrilateral ABCD is a parallelogram. Complete the statements to prove that line AB ⩭ to line CD and line BC ⩭ to line AD.

STATEMENT REASON

1. Quadrilateral ABCD is a parallelogram. given

2. AB∥CD and BC∥AD . definition of a parallelogram

3. Draw line AC . Line AC is a transversal
that two pairs of parallel lines, AB and CD
andAD and BC. Drawing a line segment

4. ∠CAB is congruent to ∠ACD and ∠BCA is
congruent to∠CAD . ? ?????????

5. m∠CAB =∠ACD and ∠BCA = ∠CAD . ??????????

6. AC = AC . Reflexive Property of Equality

7. ⊿ABC is congruent to⊿CDA. ASA criterion for congruence

8. AB is congruent to CD and BC is congruent to AD. Corresponding sides of congruent triangles are congruent.


missing proof for 4 and 5

Need Help Quadrilateral ABCD is a parallelogram Complete the statements to prove that line AB to line CD and line BC to line AD STATEMENT REASON 1 Quadrilateral class=

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Answer:

4) Alternate  Interior angles 5) Parallel lines property.

Step-by-step explanation:

The question is asking us to Complete the statements to prove that line AB ⩭ to line CD and line BC ⩭ to line AD.

In statement 4 .∠CAB is congruent to ∠ACD as AB is parallel to CD  and ∠BCA  is congruent to∠CAD as AD is parallel to BC  and these are Alternate interior angles to the parallel lines .

In statement 5.m∠CAB =∠ACD and ∠BCA = ∠CAD as by property of parallel lines Alternate interior angles are equal.

The correct quadrilateral ABCD is a parallelogram in that 4 and 5 have the same meaning for a similar triangle.

What is the quadrilateral?

The polygon has four sides and four vertices. The sum of angles is 360. The parallelogram is a type of quadrilateral in which opposite sides are parallel and equal.

Given

A quadrilateral ABCD is a parallelogram.

How to verify the statement?

AB is parallel to CD and BC is parallel to AD.

Hence it is the condition of a parallelogram.

The parallelogram is a type of quadrilateral in which opposite sides are parallel and equal.

Here ∠CAB is congruent to ∠ACD and ∠BCA is congruent to∠CAD

Then [tex]\rm \Delta ABC[/tex] is similar to [tex]\rm \Delta ADC[/tex].

similarly, ∠CAB = ∠ACD and ∠BCA = ∠CAD

Then [tex]\rm \Delta ABC[/tex] is similar to [tex]\rm \Delta ADC[/tex].

But AC = AC

Then [tex]\rm \Delta ABC[/tex] is congruent to [tex]\rm \Delta ADC[/tex].

Thus, 4 and 5 have the same meaning for the similar triangle.

More about the quadrilateral link is given below.

https://brainly.com/question/25240753

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