Given: ad ≅ bc and ad ∥ bc prove: abcd is a parallelogram. statements reasons 1. ad ≅ bc; ad ∥ bc 1. given 2. ∠cad and ∠acb are alternate interior ∠s 2. definition of alternate interior angles 3. ∠cad ≅ ∠acb 3. alternate interior angles are congruent 4. ac ≅ ac 4. reflexive property 5. △cad ≅ △acb 5. sas congruency theorem 6. ab ≅ cd 6. ? 7. abcd is a parallelogram 7. parallelogram side theorem what is the missing reason in step 6?

 Given: AD ≅ BC and AD ∥ BC

Prove: ABCD is a parallelogram.

 Statements                                                                 Reasons

 1. AD ≅ BC; AD ∥ BC                                              1. given

 2. ∠CAD and ∠ACB are alternate interior ∠s          2. definition of alternate                                                                                    interior angles

3. ∠CAD ≅ ∠ACB                                                    3. alternate interior                                                                                          angles are congruent

4. AC ≅ AC                                                              4. reflexive property

 5. △CAD ≅ △ACB                                                  5. SAS congruency                                                                                                   theorem

6. AB ≅ CD                                                            6. Corresponding Parts                                                                                   of Congruent triangles are                                                                               Congruent (CPCTC)

7. ABCD is a parallelogram                                  7. parallelogram side                                                                                         theorem

Given: It is given that and .

To Prove: ABCD is a parallelogram.

Statements                                                                            

1. and           

Reason: Given                                      

2. are alternate interior angles      

Reason: Def of alternate interior angles

3.                                                

Reason: Alternate interior angles are congruent

4.                                                             

Reason: Reflexive property

5.                                                 

Reason: SAS congruency theorem

6.                                                       

Reason: Corresponding Parts of Congruent triangles are Congruent (CPCTC)

7. ABCD is a parallelogram                                  

Reason: Parallelogram Side Theorem

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

(23*2)-12=x     x=34

step-by-step explanation: