Given AD = BC and AD parallel BC Prove ABCD is a parallelogram proof

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

7 0

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

natka813 [3]3 years ago

5 0

Answer: the ABC is up illogic of the Paul Graham that makes the box square root to DC=BA

Step-by-step explanation:

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DanielleElmas [232]

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3 years ago

Two groups of students were asked how far they lived from their school. The table shows the distances in miles: Group A (distanc

iogann1982 [59]

The mean is equal for Group A and Group B.

<h2>Given </h2>

Two groups of students were asked how far they lived from their school.

The table shows the distances in miles:

Group A (distance in miles) 1 1.5 3.03 3.2 2.8 1.5 1.8 2.5 2.2

Group B (distance in miles) 2 2.5 3.23 1.3 1.8 2.4 3 1.5 1.8

The mean of any data set or observation is equal to the sum of all the observations and divided by the number of observations.

The formula used to calculate the mean is;

$\rm Mean = \dfrac{Sum \ of \ all \ observation}{Number \ of \ obrservation}$

The mean of group A is;

$\rm Mean = \dfrac{Sum \ of \ all \ observation}{Number \ of \ obrservation}\\\\\rm GroupA \ mean = \dfrac{1 + 1.5 + 3.03 + 3.2 + 2.8 + 1.5 + 1.8 + 2.5 + 2.2}{9 }\\\\\rm Group A \ mean=\dfrac{ 19.53}{9}\\\\ Group A \ mean = 2.17$

The mean of group B is;

$\rm Mean = \dfrac{Sum \ of \ all \ observation}{Number \ of \ obrservation}\\\\\rm Group B \ mean = \dfrac{2 + 2.5 + 3.23 + 1.3 + 1.8 + 2.4 + 3 + 1.5 + 1.8}{9} \\\\Group B \ mean = \dfrac{19.53}{9}\\\\ Group B \ mean = 2.17$