Answered

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 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

  1. ∠CAB is congruent to ∠ACD and ∠BCA is

congruent to∠CAD . ? ?????????

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

  2. AC = AC . Reflexive Property of Equality

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

  4. 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. Quadrilat class=

Verified Answer :

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 \(\rm \Delta ABC\) is similar to \(\rm \Delta ADC\).

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

Then \(\rm \Delta ABC\) is similar to \(\rm \Delta ADC\).

But AC = AC

Then \(\rm \Delta ABC\) is congruent to \(\rm \Delta ADC\).

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

Related Questions