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In the diagram, a∥b

𝑎
∥
𝑏
and e∥f
𝑒
∥
𝑓
. Sylvia writes a proof to prove that opposite angles, ∠6
∠
6
and ∠11
∠
11
, are congruent in the parallelogram. Drag and drop the statements and reasons into their correct locations in the two-column proof.

(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Statement Reason
1. a∥b
𝑎
∥
𝑏
and e∥f
𝑒
∥
𝑓
given
2. Response area Corresponding Angles Theorem
3. m∠5+m∠6=180°
𝑚
∠
5
+
𝑚
∠
6
=
180
°
and m∠9+m∠11=180°
𝑚
∠
9
+
𝑚
∠
11
=
180
°
definition of linear pair
4. m∠13+m∠6=180°
𝑚
∠
13
+
𝑚
∠
6
=
180
°
and m∠13+m∠11=180°
𝑚
∠
13
+
𝑚
∠
11
=
180
°
Response area
5. Response area Transitive Property of Equality
6. m∠6=m∠11
𝑚
∠
6
=
𝑚
∠
11
Response area

3 answers

Here’s how to complete the two-column proof, including placing the correct responses in the response areas:

| Statement | Reason | |-----------------------------------------------|-------------------------------| | 1. a ∥ b and e ∥ f | given | | 2. m∠5 + m∠6 = 180° and m∠9 + m∠11 = 180° | definition of linear pair | | 3. m∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | Corresponding Angles Theorem | | 4. m∠6 = m∠11 | Transitive Property of Equality| | 5. m∠6 = m∠11 | conclusion (angles are congruent) | | 6. m∠6 = m∠11 | conclusion (angles are congruent) |

Now to ensure clarity for the response areas:

  • Response area 2: Corresponding Angles Theorem
  • Response area 5: Transitive Property of Equality

This arrangement highlights that angles ∠6 and ∠11 are congruent due to their relationship defined by the parallel lines and the properties of angles formed.

Make a family tree with at least 10 family member words

Spanish

Here’s a family tree using Spanish vocabulary for various family members. This example includes at least 10 different family member terms:

  1. Abuelo - Grandfather
  2. Abuela - Grandmother
  3. Padre - Father
  4. Madre - Mother
  5. Hijo - Son
  6. Hija - Daughter
  7. Hermano - Brother
  8. Hermana - Sister
  9. Tío - Uncle
  10. Tía - Aunt

You can visualize this family tree as follows:

                    Abuelo - Abuela
                       /         \
                  Padre          Tío - Tía
                /     \      
           Hijo      Hija
         /      \
    Hermano    Hermana

This tree shows the relationships and how the family members are connected to each other.